Hi,
If your wife did not receive a National Insurance number until 2011. The earliest year she could potentially pay for would be the 2010/11 tax year (if the number was created 5th April 2011 or Prior) or the 2011/12 tax year (if the number was created 6th April 2011 or after).
However, HMRC does not determine the amount of qualifying years a person needs for their state pension or which years will and wont benefit a person. This is all Administered by Department for Work and Pensions.
You will have to direct your query back to the
Future Pension Centre.
Thank you