This would probably be simpler just moving the server inhouse. You can do what you want with some trickery though.

Install a local mail server, and make it think it's in charge of a different domain, eg internal.example.com. Then configure accounts on that server for the finance people.

To get outgoing mail working, just configure the finance computers to send mail through that server, but still claiming to be [email protected]. There should be no issues with that. It's probably easiest to configure the internal server to relay all mail through the server at the ISP end.

To get incoming mail working, set up forwarding for each user on the external server which sends mail to [email protected]. That will end up on the internal server where the finance users can get to it.

The hardest part in all of this is getting the MX records right so that the ISP's server knows how to forward mail to internal.example.com.

Note that by doing this, you're potentially going to break a whole bunch of advanced Exchange functionality like calendar sharing and meeting invites. Not sure how to avoid that; Exchange-specific stuff isn't really my thing.