Announcing OAuth 2.0 support for IMAP and SMTP AUTH protocols in Exchange Online

Not sure I understand your setup, but the immediate question appears to be whether the external host does support mail-out using OAuth2 in addition to Basic Authentication. If so, it should be straightforward to email direct to the mailboxes  - whether internal or external - of your internal users.

Or if it is the external host mailing a MSFT 365 email account BUT your internal users are using another (not 365) mail service, the only obvious issues are that of checks against open relaying and how the external host sender is identifying the final addressees.. 

Perhaps I just misunderstand your configuration - sorry.    

Vide my preceding post, one nuisance restriction is the need to regenerate a refresh token every 90 days or less, unless the host email system requests and stores a replacement refresh token along with each access token.

My reading of MSFT’s current documentation of refresh token lifetime is that provided a refresh token is USED every 90 days or less and sometime within each 90 days a new refresh token is requested, there is no need for the app client to re-authenticate regularly.   But I am willing to be corrected on this!