Bumba, no way. It is the captain who decides. The right hand seat pilot, being F/O by status (and it does not matter if this is a TRI or LTC) remains a F/O in this scenario.
The person in the left seat should be trained accordingly BEFORE he enters the airplane left seat, thus he is captain and fully responsible.
I can only think of non-simulator training of having someone in the right seat assuming command and issue orders in such a situation.