An LPR can travel out of the US.
The frequency of travel and lenght of absences is what draws the attention of the immigration officers at the POE.
Filing taxes is not enough he has to maintain residence in the US.
If he does not wish to do so he does not need LPR status.
It is well known that many people cross over the border to file taxes and return or simply have taxes filed on their behalf, this is not enoug evidence.
No one can guarantee that he will not be questioned by the immigration officer at the POE.
It is advisable to contact an immigration lawyer to have your concerns addressed.
This is their job!