You cannot convert an assembly cut into a part cut, but you can see an assembly cut into a part. Follow me:
(Pro/ENGINEER 2000i)
Go to your assembly and redefine your cut. Choose INTERSECT PARTS->DEFINE->now from INTRSC OPER choose REMOVE MODEL->ALL->CONFIRM.
Now choose VIS LEVEL->PART->DONE->ADD MODEL->choose your part->DONE SEL->DONE->OK
It's important to remove all intersection done by the assembly cut and then to select the visibility level and at the end to select the part you need to intersect. If yu try to redifine the VISIBILITY LEVEL without removing the parts, Pro/E will not show the modification. I don't know if is a bug or not, but for sure will give you a headache.
Now, if you load the part intersected by the assembly cut, you will see the cut in your part.
Be careful if you assembled this part in several places! Now, The part has the cut!
... and there is a link now between your assembly and the part.
If you must make the cut at the assembly level and have the cut shown when the part is opened by itself (without the assembly), then make the assembly cut as before, but make sure to pick the VIS LEVEL as PART, then ADD MODELS and pick the part.
If the part is opened with the assembly, the cut feature remains frozen.
If you want to transfer the cut to the part, and break all links to the assembly, then make the same cut on the part, but while working in the assembly. Be sure to work on the part (select Modify /Modify Part / Feature, ...) or pick in the part in the Model Tree and right-click INSERT FEATURE. When making the cut, select the assembly cut edges as sketcher references and make select USE EDGE, or just trace over the edges to make the new section. Then DELETE all the sketcher references so as to add dimensions for the part-level cut.
