It will probably be fine, but they should explain the situation in the mail if possible. They can also ask for a confirmation from the person at their company email address. That is a bit of a fudge on the regulation, but probably not enough to cause problems.
If they have some visibility at the company website then that might help also.
But, universities realize that these sorts of things happen and are likely to be fine with it since you have no control.
The senior can also check with HR about the proper interpretation of the policy. It might be easier than you think. It might require that the senior show the letter to HR before sending it with "official" resources.