Bjorkman joined Briton Murray's team in March.
"Nice to have Amelie back in the team out in Dubai," Murray, who is competing in the International Premier Tennis League, said on his Facebook page on Wednesday.
"Thanks to Jonas for helping out this year. I enjoyed working with one of the nicest guys on the tour, bring on 2016."
Former world number one Mauresmo gave birth in August but will return to work with Murray for 22 to 24 weeks next year.
"Amelie did come in at a difficult time, when I had just come back from back surgery, which was tough," Murray, who will become a father in February, told the BBC.
"When I started working with her officially I was ranked 11 in the world -- I had just dropped out of the top 10 for the first time in eight years -- and I'm now back up to number 2, which is my highest ranking."
(Reporting by Martyn Herman; Editing by Ken Ferris)
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