Send reference letters from mathjobs to other positions
Short answer: no.

As suggested by user4050, I contacted Mathjobs directly and they answered the following:


  Hello Sebastien,
  
  Applicants do not have access to the letters uploaded into MathJobs.
  There is some import capability between MathJobs and
  AcademicJobsOnline, but you do not have the ability to export your
  letters otherwise.
  
  If you need anything else, please let me know.
  
  Regards,
  
  Kim Kuda
  Senior Program Coordinator