Work permit moving jobs,

Regardless of who paid for it, the work permit is not a permit that allows you to work, but a permit that allows a particular company to hire you.  Your name may be on it, but it is your employer's permit.  They also need to keep it on the premises so that it will be available for government inspectors.  When your permit comes through, ask for a copy and read it carefully.

The good part, at least according to what my lawyer told me, is that after your first permit comes through, obtaining a second one for another company is mostly a matter of submitting a new application and contract.  The other information, like the diploma, health check, and such can transfer.  For that reason, I would strongly suggest that you hang on to your current job until your work permit comes through, then have your new employer apply for a new one based on the last.