I'm not somone in the know, but unless if that's written into the EBA, wouldn't the company resist allowing FO moves from the Ejet to the 737? Please correct me if I'm wrong, but wouldn't that drastically increase training cost through endorsements and lost line time if they effectively have to double the training? i.e. train an existing ejet FO onto the 737 (at the company's endorsement expense) - lose the pilot in the meantime - then train a new FO onto the Ejet to replace him/her?
Wouldn't it we easier to just train a new recruit directly on the 737 if that's where the crew are needed?