As part of its parameteres, Move-ActiveMailboxDatabase also has the -ActivatePreferredOnServer parameter, as stated in the cmdlet's Technet page. Its description read "The ActivatePreferredOnServer parameter specifies the name of a Mailbox server on which to activate all mailbox databases that have copies with an ActivationPreference value of 1. You can use this parameter as part of ending maintenance mode on a Mailbox server." Since I didn't really get that after reading it a few times, nor does there seem to be a mention around the web aside from that Technet page, I though about testing it in a lab with a 3-site-stretched DAG. However the parameter isn't recognized.
Next I've tried figuring out if there's any problem with the management role assignment that grants permissions to this cmdlet. The user running it in the lab was the built-in Administrator account, which is a member of Organization Management. In identifying the management role that includes this cmdlet, I've followed the redirection on the aforementioned page, which links here. Yet none of the management roles specified there contain Move-ActiveMailboxDatabase as entry; actually it turns out that "Databases" is the only role that has it from the list that are assigned by default to the "Organization Management". However the entry in this role doesn't contain -ActivePreferredOnServer in its parameter list, which makes it pretty clear why it wouldn't work in the first place.
I also thought about the delegating only role assignments, since Organization Management has a couple of powers governed by various roles which it cannot directly use. Mailbox Search is one of them. But there's no mention of this parameter for the Move-ActiveMailboxDatabase cmdlet.
Did anyone ever use this parameter ?