Acquisition Creates a debacle...

My company has acquired a portion of a company.  That company is all confined in an OU within the parent domain.  We are only getting the OU information out...security groups, Usernames, etc that have pertinence to that Company.  Those users in that OU are already on O365 and have the main company tenant alias....onmicrosoft.com and also the alias for that company that we acquired.  What would be the easiest way to transition those users into our tenant with the least downtime for the users?