I recently moved from California to Ottawa on a closed work permit. Same situation, it’s just that my H1B was expiring beyond 6 years so there were no more extensions left, and I didn’t have my PERM filed.
Regardless, you would be working for an employer from Canada, so you they would be paying you the compensation in CAD, not USD. You would be liable to pay tax in Canada for any income you earn worldwide as I believe you will be a tax resident of Canada. They will also have to issue you a T4 for the tax year for you to file your tax return with CRA.
There will be some situations like stocks/ESPP/RSU/Bonuses etc. where a double tax might be applicable depending on where you earned the capital gains. In such cases, you will be able to get a credit back for ssome portion when you file your return the following year.