They'll have to operate Songbird as Songbird for quite a while to show the FAA that everything's performing as designed in the current manuals and Op Specs. Then they can start making changes such as name change, location, different aircraft. It's a very painful and slow process in my experience and I don't think there's any certificate transfer involved here.
It definitely can work but IMO it would have been easier to just get the certificate on their own where they wanted, with a fairly new aircraft and a really experienced 119 management team.
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