Maybe I’m missing something.
I thought he had at 20-amp receptacle that was bad, and he wants to replace it. If it is for only a microwave, a 15-amp receptacle will be fine, even if it is on a 20-amp circuit.
Or he wanted to go to a 20-amp receptacle for reasons that I cannot image, unless his appliance has a 20-amp plug which I see as extremely unlikely.
Now, if his microwave has a 20-amp plug and he wants to upgrade to match the plug, he will need to upgrade the wire as well as the breaker.
The breaker is sized to fit the wire. 14-ga wire = 15-amp breaker. 12-ga wire = 20 amp breaker.
A 20-amp receptacle will be fine with 14-ga wire and a 15-amp breaker. In this instance the receptacle would be more than is needed, but it would not be unsafe, unless someone tried to pull more than 15 amps through the circuit. In that case, the breaker should trip before the wire is overloaded.
Now, if you increase the size of the breaker to 20 amps, but keep the original 14-ga wire, you are asking for an electrical fire from overloading the wire.
Wayne