Pls ask me i really need to know this. After the engine CFM56-3C start and light up can i disconnect it's starter from it? In order to put it on onother engine for starting process?! Thank you in advance.
What's suggested amounts to taking an engine apart while it is running. The amount of risk involved for the mechanics would be immense, if it's even possible at all.
If one makes enough assumptions about what risks one is willing to accept, what condition the running engine is in afterwards (presumably still running, not necessarily airworthy), how extensive the preparations are for such a stunt (i.e. somebody may have to create a procedure & checklists from scratch), and so on, all sorts of crazy things can be possible to do.
But as far as remotely practical or safe, no, taking something as big as the starter off of a running engine isn't something you're likely to see happening.
Some turboprops (the C-130, for one) can start the engine with the starter removed -- a high-speed taxi up to about 100 knots and then a gentle abort, on a sufficiently long runway is all that's needed. But pulling (and padding!!!) the starter from a running engine? No, thanks!