I was playing London on my desktop at home and now have to travel and was hoping to load it up on my laptop. After downloading it, the game had the London loading screen but loaded me into my FO4 autosave. I dont care about the FO4 autosave as it was years ago, how do I get my saves to transfer back and forth?

GOG Galaxy client should handle that I think (i personally dont use it) - however the save space is rather limited as I understand.
Similarly installing something like dropbox across your devices and targeting the save location may work.
Hopefully somebody else can give you a much better answer as this isnt an issue for me.