Does the PMK gas mask filter contain any asbestos?

So long as you purchase a filter designed specifically for the PMK, since these were made somewhere between the late 80's and early 90's, no, they do not contain asbestos.

However, gas mask filters have life spans of only a few hours once they are used for the first time. They can be stored for some years, but as soon as a breath is taken through them, the clock begins ticking. In most cases the average filter life is roughly 40 total use hours before the contents of the filter become saturated and unable to remove harmful gases from the air.

The safest thing to do is never breath through a gas mask filter unless you have to. Never breath through one for long periods of time, and NEVER use a filter or mask purchased at a surplus store or on-line to attempt to protect against actual threats (biological / chemical agents). 99.9% of masks found in surplus stores have either been used in military exercises, or have defects which lead them to your hands. Never trust a mask that was not specifically fitted for you in person. Even 1mm of space between your face and the mask can allow harmful agents to infiltrate and turn your mask into a gas chamber.