Custom in what sense? If it's made by dialing in morphs, use the free Poser Format Exporter script from the DAZ store to save a pz2 or fc2 (face) file, including the morphs but not the transforms.

If you made it with DForms in DS zero the pose (and all but the custom morph), hide all but the affected part and export as OBJ with the Poser preset and Exclude invisible selected in the options (or if it spans multiple parts you'll need to do this for each part in turn), then in Poser select the part and import the OBJ as a morph target 9from the Object menu or the proerptioes panel). If you want to share the morph then the pose is no problem, but for the OBJ approach you need to open the OBJ in a text editor and remove all but the lines starting with v (as long as there are no morphs you didn't make included - if there are then you need to separate out your contribution from the other morphs). There are also some scripts that will help, but they play better with DS2 than DS3.