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 toyour 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.