Odd SSL request
Hello everyone,I have ran into something today that I have never heard of doing before

I have this customer that does business with sprint. Now sprint provided them with a URL that they want them to use, I guess they pointed the DNS to my customers IP/hostname because when you goto that sprint address, it pulls up my clients site.
Okay so now, what sprint is requesting them to do is put an SSL for that URL on my server...............now at first I was like, what the heck?
Is it possible to apply an self generated SSL on my server for THAT domain, so the ssl popup does not occur.
If not how can I do this? Since their URL is masking my clients site, its not using their (sprints) SSL cert.
I hope this makes sense.
Thanks for any comments or solutions!