To transfer maps between people, you must give them your .map file and the folder of your map (it will have the same name as your .map file) that is located in C:\FeralHeart\media\terrains
I noticed you already stated that ^^ Just be sure that those two are placed in the correct locations and make sure that the person you are working on the map with gives you their folder and .map file when you need to go back to editing after they've made changes.
As for objects:
If you have any custom objects used in the maps, make sure that the other person has all of the files that make up an object that you have and that they put them in their my_objects folder. This would include the .mesh files, the material files and the texture files.
Not only that but they will need the .object file (which is the object group that will be listed in your map maker/object maker). So, if I were you, I would just give them the entire contents of your my_objects folder in a zip to ensure they have everything that you have and not only that but give them the .object files that you know are your custom packs (which will be the object group). These .object files are located in FeralHeart\media\objects. You will notice that each of these files are object groups that you have in your map maker/object maker.
I hope all of that makes sense. Let us know if you have further questions or if I wasn't clear enough on something ^^