Have a damaged outlet of an electrical extension cord set at 125volts 10Amps. Want to know if I could replace the outlet with a rating of 125volt 15 Amp. Will that be possible?

You will not like my answer, but it is the correct one.

A damaged extension cord should be taken out of service.

Any modifications will violate the UL Listing of the product.

Now, has anyone repaired a cord before? Sure, of course, thousands of times.

The receptacle configuration for a 10 amp outlet is the same as a 15 amp, just that it is rated 5 amps more. The entire cord is only rated 10 amps, that is why the outlet is rated the same.

So, if you decide to continue to use a repaired cord, you assume all risk.