Thank you for your answer.

Yes, I am sure that it is a 250AMP breaker in the 500AMP service panel.

You wrote, "use 3-#250 MCM XHHW and 1#2 XHHW in a 3" PVC SCH 40 PVC conduit."

Does it mean 3 wires #250 Gauge AWG and 1 wire #2 gauge AWG (Stranded Copper) to the sub panel?

Thank you in advance.
Buddy1

Oops sorry I meant to add copper to my answer. Yes 250 MCM is a AWG wire gauge size.

If you want to use aluminum, then 300 MCM wire will work.