Do I have to keep my source domain open?

If you want to forward email from a source domain, you’ll have to set keep the domain(s) open that manage each user account. See this guide to set up domain-wide forwarding.

Alternatively you can use an MX forwarder to forward messages to addresses at those domains to¬†your new domain. An additional option is to close the domains and add them as domain aliases and create groups for the addresses you’ d like to continue to receive mail to.