Not trying to police anything, but if you have a legitimate, licensed version of Final Cut Studio on your iMac, it was installed from a set of disks _ not a download.
That license allowed users to install on one desktop and one laptop, So those same disks should be used to install the apps, including the "old FCP" on your MBP.
I don't recommend copying the apps. It will probably work fine most of the time but far too often, problems arise down the line that would be avoided by a "clean install" of the apps; then – very importantly –successively running Software Update until there are no more updates.
If you would like more input on this, post over at the Final Cut Studio forum.
Good luck.
Russ