Function modules, like other ABAP workbench entities, are client-independent. That is, you do not need to copy them between clients on the same instance.
However, you can find the transport request that contains your changes by going to transaction SE37, entering the name of your function module, and then choosing Utilities -> Versions -> Version Management
from the menu.
Provided you did not put the changes into a local package (like $TMP
) the system will have asked you for a transport request when you saved or activated your changes, that is, unless the function group is in a modifiable transport request, in which case it would have created a new task for your user under that request which will contain you changes. To check the package, use Goto -> Object Directory Entry
from the menu in SE37.