Tax Mistake During Application in Process

Dear Friends,
I could not find the help on topic and posted a new topic.Please help
My wife EU National was part-employed and part self-employed during 2010----2015.Today received a letter from HMRC saying that there is discrepancy in taxes paid 2015.

Her employer showed taxes (which I guess maybe right)
She added her wages slips as she misplaced P60 and I believe there were two missing so there is £300 difference in taxes.
Now We asked for a copy of P60 from her employer, she will pay that taxes if she added and paid less taxes.
But should she inform HO or just correct the taxes and HO can check it themselves?
please help!!!