Running Outlook on a Different Domain

We have 2 domains in our office, one is used by the majority of staff but we have another that's used for our back office system and there are 2 users on that domain. They are also setup on the main domain with network access, email, etc. and I'd like them to be able to run Outlook on their PC even though they're on a different domain. Is there a way to do that?

Thanks.