Letter of recommendation from a deceased advisor
I can't think of a reason why it should not be sent. The professor wrote it, his (untimely) passing shouldn't affect its being sent out. It may be a good idea to have the secretary include a note that this was written prior to the professor's passing, simply to avoid any questions of someone else writing it.

If you have specific requirements for the job process (I'm not familiar with MathJobs), contact the site and/or the places where you're applying. While unusual, this isn't that uncommon, and any respectable program should be willing to work with you on this.