CafeTran

Here's a great Keyboard Maestro macro that you can use to move your source files, TMX and/or client's glossary files e.g. from the Desktop or Download folder  to your client project folder:

https://forum.keyboardmaestro.com/t/finder-move-selected-finder-items-to-choose-folder-example/4630

I place everything on the Desktop, press the keyboard shortcut and select the client folder in the prj tree.

You'll have to adapt the path here:

BTW: I've disabled the confirmation request.

Lenting: ...great gif movies that can't be paused

Great they are, and they don't have to be paused, because they are so short even you should be able to understand what's going on. Come to think of it...

H.

This typically is an action that doesn't require Keyboard Maestro at all (most actions don't). Automator can do the job just as well, and is a lot easier.

It shows the action in the context menu (above), and you can assign a keyboard shortcut to it. If you save the workflow as a Folder Action, so you can drop files and err... folders on it, or you can save it as an app to drop files on it.

H.

Lenting: Your Automator solution can only handle one destination folder at a time.

Because I don't need more than one. But I can add a variable as well.

H.

Lenting: Can you set it at runtime?

Why not? I can ask for a folder, an extension, or whatever, though it will require user input, of course. Did you check if JMichaelTX (Jim)'s solution works? 

H.

Lenting: Don't you test your suggestions?

Always. But I don't turn them into incomprehensible silent videos.

H.