Portable Generator Receptacle

Hello, I am a DIYer and I have a Northstar model 5500 PPG generator, item number 165911, whose wiring was modified to replace the 120/240V 20A receptacle on the generator to direct wire to a dryer plug (3 wire). I have a new residence and have just had installed an exterior receptacle to plug my generator into (by a licensed electrician) to eliminate the back feed issue. The generator is now to plug into a 30 amp 3 pole 4-wire twist lock connector (male).

I can determine from the generator wiring diagram and from how the wires are configured now as to how to disconnect the dryer plug electrical cord and replace the 120/240V receptacle that was originally installed (L14-20R). Can I just replace the original 20A receptacle with a 30A receptacle, wired the same, and be OK? I would then get a suitable cord to run between the generator and the new house hookup. Other options?

Thank you.