Looking for advice on having an extension of stay transferred to a new passport when re-entring with a multi-re-entry stamp in an old passport.

I have a Non-Imm B (BOI) with two-year extensions of stay, but I plan to get a new passport in Australia in February - it's easier to do it there vs. Thailand. My Thai legal employer tells me that I should show both passports (old and new) to the Immigration officer on arrival at Chiang Mai International Airport and ensure I get stamped into Thailand in the new passport with my current extension of stay.

Is this correct? I've read various other reports about needing to go to immigration for stamp swaps, but can I do it on arrival at the Immigration counter? I know the other requirements to change passport numbers with my Work Permit, etc.