Exchange On-Premises cross forest migration

Hi Folks,

A customer has on-premises Exchange 2013 with SMTP domain (abc.com) and AD 2012 domain "alpha.com". It also has Hybrid Exchange setup. Due to business requirements, customer will have AD 2019 as "beta.com" and will keep SMTP domain (abc.com) with Exchange 2019 on-premises.

For user mailbox and computer migration to new AD Domain, Quest tool will be used after establishing trust between both AD Forests. My concern is, how we will do email routing while keeping the same SMTP domain which is (abc.com) during co-existence? Any suitable link or guidance is appreciated. Thanks.