On the Import Screen in iMovie, you specify where the clips are stored.
The default location is in the Movies/iMovie Events/<your event name> folder on your boot drive.
You can also import to the Movies/iMovie Events/ folder at the top level of any other drive that is formatted as Mac OS Extended (journaled).
To put the Event onto an external drive so she can use them, see this post.
By the way, the reason your client probably could not use your MOV files...
Did you capture them in ProRes422? iMovie does not come with Pro Res 422 codec.
You can transcode them to Apple Intermediate Codec and they should work.
But capturing in iMovie amounts to the same thing. They will be captured in Apple Intermediate Codec.