$ mkdir -p ~/.steam/steamapps/compatdata/24980/pfx/drive_c/users/steamuser/My Documents/BioWare/Mass Effect 2/Save/ME1
$ cp -vr ~/.steam/steamapps/compatdata/17460/pfx/drive_c/users/steamuser/My\ Documents/BioWare/Mass\ Effect/Save/* ~/.steam/steamapps/compatdata/24980/pfx/drive_c/users/steamuser/My Documents/BioWare/Mass Effect 2/Save/ME1

The Mass Effect save should now be available for import in the Mass Effect 2 New Game interface.

The path prefixes here are the WINE prefixes used by Proton. 17460 is the Steam game ID for Mass Effect; 24980 is the Steam game ID for Mass Effect 2.

This quick tip brought to you by information from https://answers.ea.com/t5/Mass-Effect-2/PC-Importing-a-save-file-from-Mass-Effect-1/m-p/5810699#M7696