Sorry, it doesn't work like that.
Most programs (other than 'portable' ones) need to be 'installed' on a computer, which involves changes to the registry. You can't just move the program file across from one computer to another. (If that wasn't the case, software piracy would be rife. For example, someone could pay £725 for the latest version of QuarkXPress and then give away unlimited copies, free of charge, to his friends).
So your suggested solution to your problem simply won't work.
Windows 10 Mail has been widely criticised as being too basic for many people's needs. Annoyingly for those people, Microsoft no longer offers Microsoft Essentials as a download. However there's always been a far better program available, so it seems the obvious choice to use:
https://www.thunderbird.net/en-GB/