Letter of recommendation from a deceased advisor A PhD advisor usually sent all his letters of recommendation for his students through his secretary. He wrote a letter for his PhD student who is currently applying for academic positions, and unexpectedly died a month after. The secretary has a letter. Should this letter be submitted as a part of application? Should it be stated in the cover letter that the letter is from a deceased advisor and how the submission should be handled (for example, for MathJobs should an account with the secretary email be created)? 

The advisor worked in the US and the applicant is considering both American and European universities.
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.