I move figures/characters/clothes from DAZ to Poser all the time. Many G2 products have Poser Conversion Files, and if you go through your product library and download them to your Poser runtime, they will appear in Poser. But here's the rub. You have to rely on DSON to run DAZ native G2 figures and kit in Poser, and DSON is always an iffy proposition. It's slow and unreliable.

My solution is to convert my DAZ figures to native Poser ones. You can do this with people and clothing. You will need to buy Netherworks Creators Toybox at Hivewire3D, which has instructions on the fairly simple procedure for converting your DAZ stuff so it will act like anything else in Poser. If you look for my posts at Hivewire's forums (this place won't allow me to link to the other site), I've described the process in step by step terms because the Hivewire world includes Poser and DAZ users who get along and help each other out.

A native G2F or G2M figure will play well with the fitting room because it has real Poser rigging.

For G2 outfits that don't have Poser CF files, it's a simple matter to export them from DS as cr2's and run the Toybox on them. Presto: Poser native! I also have had no problem exporting obj's of Genesis 3 clothes and importing them to rig in the fitting room or the setup room. Exporting the loaded item from DS as an obj carries the materials with it. Is that how you are exporting your obj's?