Well they should be able to do it, but...
Tell your new employer to help you create a new HSA and have them contribute to your new HSA. But note that you can continue to take distributions from your old HSA (pay for medical expenses) until the funds in the old HSA are exhausted. At that point, you can close it. Then you can use the new HSA exclusively.
There is no problem with having two HSAs - you can contribute to both (if your employer agrees) and pay out of both. or contribute to one and still pay out of both, until the other runs out of funds.
