I tried your suggestions but still having problem with the 2 Lumia 640's.
When I go to SETTINGS, ACCOUNTS, Your email and accounts, the Microsoft account shows up in the list of Email, calendar, and contacts list along with the other Hotmail, 2 Gmail and 1 yahoo account. All have an envelope icon except the other Hotmail account which has a Outlook icon. When I go to the Outlook mail app there are 4 accounts, 2 Gmail, 1 Yahoo and 1 Hotmail, NOT the Microsoft account on the phone. So I am in the Outlook mail app and go to ADD an account to the 4 that are listed. I've gone through setting it up choosing Outlook.com; Exchange; Other account and even Advanced setup and they all come back and say All done! Your account was set up successfully. I click on DONE and the only time it shows up in the list of email accounts is when I set it up using Advanced Setup. If I go to SETTINGS, ACCOUNTS, Your email and accounts, I now have another account with the same address as my Microsoft account but it doesn't sync and it doesn't have a sync option for Calendar or Contacts, only Email button. So I am unable to sync my Calendar and Contacts with my Microsoft account. I can only sync my calendar and contacts with the other Hotmail account which works but that is not the account I want to sync with.
Sorry this is so long but that's the problems I'm having. I took the Lumia 640 out of the box and upgraded to Windows 10 version .63 BEFORE I started loading my info and accounts, maybe I should have loaded everything in Windows 8.1 before I upgraded to 10. That's the only difference between the two phone setups.
UPDATE: I finally gave up and did a HARD reset on one of the 640's and I now have my Microsoft account showing all of my Mail, Calendar and Contacts. I read on this forum that a HARD reset would fix the problem and it did.