It depends. By default, Azure AD only allows UPN for login ID. When UPN and email are the same, Azure AD B2B invitations and subsequent sign-ins work as expected. However, issues can arise when a user’s email and UPN don’t match, and the email is used instead of the UPN to sign in.
When a user is invited with a non-UPN email, they will be able to redeem the invitation if they redeem using the email invitation link, but redemptions via a direct link will fail. However, even if the user successfully redeems the invitation, subsequent sign-in attempts using the non-UPN email will fail unless the identity provider (either Azure AD or a federated identity provider) is configured to allow email as an alternative login ID.
This issue can be mitigated by:
Enabling email as an alternate login ID in the invited/home Azure AD tenant
Enabling the federated identity provider to support email as login ID (if Azure AD is federated to another identity provider) or
Instructing the user to redeem/sign-in using their UPN.
To avoid this issue entirely, administrators should ensure users’ UPN and email are the same value.