Congrats and welcome to Amateur Radio.
One caveat on applying for your living relative's former call...BE CAREFUL to NOT, repeat NOT use the "deceased relative" or "former holder" options on the FCC form 605. As another poster said you'll be applying for an available Vanity call like anyone else, but the FCC will eventually catch the mistake and sends you one of those nasty letters to "show cause" why you applied the way you did, then make you go through a confusing paperwork drill to get it right.
Thanks for the tip Steve! It's my son wanting my old call and I'll be sure to warn him not to make that mistake. I can see how that could happen.