Currently, only the board owner has access to Outlook integration. Each user should be able to connect to Outlook using their own credentials to send emails from their respective email accounts. Please enable Outlook connectivity for all users, even if they are not board owners.
We had this problem as well, but luckily we found out what is causing it in our case.
In our case this was caused by the following setting:
Create and edit automations and integrations
If you disable this on a board for members, only board owners will be allowed to link their outlook accounts through that board.
They will however still be able to set it up through another board where this option is enabled for members.
Hope this helps you as well.