The Tween morphs, for example should be here:

DAZ 3DStudioMy LibrarydataDAZ 3DGenesisBaseMorphsMurgatroyd

Can you see them there?

In Shaping with Genesis selected, the head morphs, for example, are in the Head section, or in Parameters, under Actor/Head. In Parameters you will see them here unless Genesis is selected at the root "Genesis" in the Scene tab, but not if any node (bone) of Genesis is selected separately.

The above is in Studio 4.5, I believe things are different in 4.0 in respect to what appears in Parameters and Shaping. Also, as I seem to recall, in 4.0, new morphs don't appear on previously saved figures (e.g. if you load an old scene) and you have to "refresh" Genesis by reloading the base Genesis figure. I expect you are already looking at a freshly loaded base Genesis, but I thought it might be worth checking.

Otherwise, I can't think of any reason why you cannot find the morphs.