There is a way to do this. First a bit of background. This used to work but a few years back FM changed their file format from .slf files to .fmf files. GS has never caught up to that, I suspect there is a fair bit of programming work involved.
Firstly check you know where the shortlists are stored, default directory in Windows is C:\Users\<<Username>>\Documents\Sports Interactive\Football Manager 2022\shortlists.
If you only want to bring in a handful of players or less there is some very easy functionality. After you have found a player you are interested in double click on the line the player is on in GS. A pop up box will be brought up for that player with more detail.
If you hover your mouse over the name in the pop up box it will say "Click to copy name to clipboard". Click the name. Now go back to FM. In middle top of most skins it will tell you what page you are on - Home, Inbox, Squad etc. If you click there you can paste the player name. FM will search for the player. Select the player if it brings back more than one, make sure the players age, team and position are the same. You can now make an offer for the player or save them in shortlists if you want.
If you have a heap of players you want to bring across to FM, firstly create the shortlist you want to make, and ensure it is in the correct directory.
Second, download FMRTE (the free version works you don't need to pay for it) and load your game.
1. At the top of FMRTE it says "shortlists" click on it
2. Click on load shortlist
3. Load the shortlist from FM genie scout into FMRTE
4. Highlight a player in the shortlist and press ctrl+A (to select every player in your shortlist)
5. In the bottom right there is an option to click which allows you to save the shortlist
6. Save as a new shortlist using whatever name you want ensuring it saves to the directory identified above.
Now you can import the new shortlist you created into FM.
Summary - make the shortlist in FMGS, import shortlist into FMRTE, save shortlist using FMRTE then import into FM via FM itself. Pretty sure this works the other way as well, just save the file as an .slf file instead of an .fmf file.