Question it.
Your qualifying weeks don't need to be consecutive and can be with different employers. The 13 weeks can be ANY thirteen weeks in the last 66 before your baby is born.
I strongly suspect someone is getting wires crossed.
www.gov.uk/maternity-allowance/eligibility
You might get Maternity Allowance for 39 weeks if one of the following applies:
you’re employed, but you can’t get Statutory Maternity Pay
you’re self-employed and pay Class 2 National Insurance (including Voluntary National Insurance) for at least 13 of the 66 weeks before your baby’s due - the amount of Maternity Allowance you get depends on how much Class 2 National Insurance you’ve paid
you’ve recently stopped working
In the 66 weeks before your baby’s due, you must also have been:
employed or self-employed for at least 26 weeks
earning (or classed as earning) at least £30 a week over any 13-week period
You may still qualify if you’ve recently stopped working. It doesn’t matter if you had different jobs or periods of unemployment.
Use the maternity entitlement calculator to check your eligibility.
Maternity Allowance for 14 weeks
You might get Maternity Allowance for 14 weeks if for at least 26 weeks in the 66 weeks before your baby is due:
you’re married or in a civil partnership
you’re not employed or self-employed
you take part in the business of your self-employed spouse or civil partner
the work you do is for the business and unpaid
your spouse or civil partner is registered as self-employed with HM Revenue and Customs (HMRC) and should pay Class 2 National Insurance
your spouse or civil partner is working as self-employed person
you’re not eligible for Statutory Maternity Pay or the higher amount of Maternity Allowance (for the same pregnancy)
If you haven’t paid enough Class 2 National Insurance
Contact Jobcentre Plus if you haven’t paid enough Class 2 National Insurance to qualify for Maternity Allowance when you make your claim (eg because you’re self-employed and haven’t filed your Self Assessment tax return yet).
HMRC will contact you to let you know how to make an early payment.
If you lose the baby
You may still qualify if the baby is either:
stillborn from the start of the 24th week of pregnancy
born alive at any point during the pregnancy