A particle's mass is the same in all inertial reference frames (even though its speed is not).

Question

Quizplus · Accepted Answer

A particle's mass is an intrinsic property and does not change with its speed or the inertial reference frame from which it is observed. This is in contrast to relativistic mass, which does increase with speed, but the concept of invariant or rest mass remains constant across all inertial frames. 
By definition (in this book) mass is frame-independent.

A Particle's Mass Is the Same in All Inertial Reference