Thank you for your patience guys. This past weekend was a bit of an emotional and physical ride for me. But I recovered and  am better now.

I am going to post here the detailed workflow, how you can transfer your previous generation characters to G3F manually. Good news is, using this method you can also create your free clones of Genesis, V4 etc for G3F, so that you can use their outfits/hair on G3F using autofit.  And lastly, once you get the hang of it and understand what you are doing, it won't take much longer. You can transfer a V4 character to G3F in just 2-3 minutes :)

Here are the detailed steps-

1. Load G3F base model, go to parameters>general>mesh resolution, set it to base with 0 subdivision. Click the display options (top left of the parameters pane) and turn on "show hidden properties". Now go to Hidden>Genesis 2 Female and dial it to 100%. This will give your G3F model the shape of G2F. If there are other objects in your scene like camera, lights, delete them. Export your G3F as a wavefront object, for simplicity use daz studio scale. You need to do this step just once for all future uses, so its better to create a separate folder and store these objs there with relevant names (I created a folder named genesis 3 and saved this obj as simply g2f inside it).

2. Create a new scene, now this time load Genesis 2 Female base model in your scene. Import the obj you saved in step 1 to your scene. You can see their identical geometries in the viewport. 

The concept is really easy to grasp what you are doing. Simply think of your obj as some kind of bodysuit, with transfer utility we will fit this bodysuit (or your imported obj) to our Genesis 2 Female figure. What transfer utility will do is it will transfer morphs from Genesis 2 Female figure to your imported obj. By dialing those morphs, you will be able to give your obj the desired shape. But your obj is still a G3F mesh and hence, you can then import this obj, modified with desired shape, as a morph for Genesis 3 Female figure.

Click on a blank spot in your scene tab to deselect everything, in the menubar go to Edit>Figure>Tranfer Utility. Select your Genesis 2 Female figure as the source and your imported obj as  target. Leave "item shape" to default. Click "Show Options", select "Use Near Vertices" with nearness to 1000%. Leave other options as it is and click accept. 

(You "may" need to convert your obj to a figure with a TriAx Weight Mapping (though I have successfully done without using this part, but sometimes DS did weird things). If needed then before using transfer utility do this- select your obj in the scene tab, in the menubar go to Edit>Object>Rigging>Convert Prop to Figure. A dialog box will pop up, use TriAx Weight Mapping. Then use transfer utility as described above)

Now we can give our bodysuit (our imported obj) any shape using Genesis 2 Female morphs. Lets say you want to transfer 2 morphs- one is a your own self created named Paula, and other one is Genesis. In the scene tab, select Genesis 2 Female figure, dial these morphs to full and back to zero one by one (you will find Genesis in Hidden>Clones). Delete Genesis 2 Female figure from your scene. Select your obj, you will find the 2 morph dials (Genesis and Paula) in the parameters. Make sure the mesh resolution is set to base with 0 subdivision level. One by one, dial your morphs to full and export them as wavefront objects (also make sure there are no other objects in your scene like camera or lights).

3. Create a new scene and load Genesis 3. Import those objs one by one as morphs for your G3F :). (In case if you don't know how to import obj as a morph see my next post). 

4. However, we are still not done (try dialing one of these morph and give her a pose :)).Zero the pose and your imported morphs. In the menubar go to Tools>Joint Editor. You can see now the detailed bone structure of G3F mesh.

Now dial 1 of your morhps to full. You can see the bone structure is not following the mesh (and that was the reason for that weird pose. Don't play with those bones unless you know what you are doing!). Right click in your viewport and select Edit>Adjust Rigging to Shape. A dialog box will pop up, select all 3 checkboxes. Click accept.

Right click on your morph dial in the parameters and click edit mode. With your morph still dialed to full, right click on it and select ERC freeze. A dialog box will pop up, select all 3 checkboxes in the Additional Options. Click accept. Now the bone structure will always follow your morph to whatever strength you dial it to.

To save your morph, go to File>Save as>Support Asset>Morph Asset(s). In the vendor name, give your name (or pseudoname) and give a name to your morph in the product name. Select your morph from the properties. Repeat this part for your other imported morphs from G2F. And thats it, everytime you load Genesis 3 Female you will find your morphs there :).

5. If you want to export your characters from Genesis 1 to G3F, method is similar. Just that, in step 2, your G3F's obj must have Genesis base model's shape and you use Genesis figure instead of G2F. To give G3F, the shape of Genesis, it is explained how you can achieve that in step 2 :).

6. Same goes for Victoria 4 models. However getting V4 shape for your G3F obj can be tricky. If you have purchased "Victoria 4 shape for G2F" or similar for genesis, you can then use step 2 or 5 accordingly to get V4 shape for Genesis 3. I think Genesis base already comes with a clone of Victoria 4 installed in it, but it doesn't transfer. What you can do is dial that clone to full, set mesh resolution to base with 0 subdivision and export figure as an obj. Import it back as a morph for genesis. You can transfer this morph then to G3F as explained in step 5 to give G3F obj, Victoria 4 shape (remember you need to do this just once).

Once you get that, you can then use step 2. Import your G3F obj matching V4 shape and load V4. Note that, when you load a V4 base, her feet are not at 0 pose. Convert her to triax weight mapping from "Edit>Figures>Rigging>Convert Figure to Weight Mapping" . Use transfer utility then as explained earlier.

7. There is a free "dawn clone for genesis" available in sharecg. Installing it means Dawn can behave as a Genesis Morph. So my guess is you can transfer your Dawn morphs to G3F too from step 5, though I haven't tested. If somebody does, please post results.  

Note:

1. If you have a character which you have made using many morph dials, say a V4 character using too many morphs++ dials, then you need to combine all those morph dials in one. To do this, set your character's mesh resolution to base with 0 subdivision (for V4, subdivision can be set to 0 if "show hidden properties" in the parameter pane settings is ON). Zero the pose (very important for V4 characters). Make sure there are no other objects in your scene and export your character now as a wavefront object, for simplicity use DS's scale.

Create a new scene and load the base model of your character. From here, if you are using a V4 character, zero her pose then convert her to triax weight mapping from "Edit>Figures>Rigging>Convert Figure to Weight Mapping" first . Now import that obj back as a morph. (In case if you don't know how to import obj as a morph see my next post). 

2. For some reason, I found injecting a morph (or importing an obj as a morph) first and then converting Victoria 4 to triax weight mapping doesn't work. Doing this in reverse order works fine.

3. For base models like V4, Genesis, Dawn its better to save them as clones rather than as morphs for G3F. This way you can also fit that character's clothing, hair etc to G3F using autofit tool. To save a clone, see my next post.

4. If you are not able to dial a hidden clone/morph (some hidden clones/morphs have min and max set at 0), then do this- click the small gear at the top right of your morph dial and click parameter settings. Set max to 100, select "as percent" and click accept.

5. Lastly, if for some reason you mess up and want to delete a saved morph of yours to start again, there will be a folder saved with your name (or the name you gave as vendor name while saving it) in "DocumentsMy DAZ 3D LibrarydataDAZ 3DGenesis 3FemaleMorphs". Delete the morphs you want from that folder only, dont mess with any other folders. Its better to save that as a backup somewhere else before deleting it.

This method is also useful if you want to transfer your previous generation characters to G2F/Genesis :).

In my testing, I found what Zevo said is true, face doesn't transfer too well but only for V4 (Genesis/G2F transferred well and I haven't tested Dawn). But still imo it gives you a good initial base to start from. You may want to tweak the cheeks a bit and especially eyelids as those 2 areas are where there is a major mismatch. 

And yes, face transfers a lot better from V4 to Genesis/G2F. Maybe it has to do with the fact that we cannot transfer our textures from previous generation to G3F as of now. Textures play a lot of role in how your characters look, even if 90% of geometry matches, textures can give a lot different looks.