There is a reason why the export to zip does not include libraries. As
@Beja tried to explain, any official library is only available to licensed users. this is so to avoid distribution without consent of paid material, being it libraries or other stuff.
For the case at hands, adding to all the "what if"s, what if the other user is using an older IDE that is incompatible with your project or libs?
I think that, in the given scenario, of co-working, either an online repo, or shared folder in a cloud service would suite better the needs.