Can’t get a Letter Of Reference with signed seal
Try contacting the program's admissions office first before submitting the application, and as long before the deadline as possible (so, immediately). They may offer a workaround. For example, they may provide an email address to which your professor can directly send the letter. Even if it turns out that they allow you to mail the letter yourself, you need to check with them first.
I did this once when in a similar situation, where I could not submit the recommendation letters in the usual method prescribed by the program, and was told of an alternative method on contacting them.