External email sending

I have a number of external clients who belong to an independant domain who wish to use their email accounts from my exchange server from these external domains.

My question is, is there anything I can do on my end to enable them to send emails from their external exchange server, through their email addresses at my domain, or is a cange required at the independant domain exchange?

eg. User is logged in to a domain abcd.com with an exchange account User@abcd.com. User also has an exchange account on my domain, User@xyz.com and wants to send emails from the User@xyz.com email account while logged in to abcd.com

What is the best way to go about allowing emails to be sent through xyz while logged in to abcd?