I know @TuragaNuva already answered this question, but I just wanted to clarify specifically why he can't.
Anything he would write that deals with G1, even if he were to call it a "fanfiction" and do it as a personal project, is still directly associated with the original IP that LEGO owns the rights to.
Considering it's LEGO's property and Mr. Farshtey (to my knowledge) is still currently employed from time to time by LEGO, the company does not want their own employee producing content for their product that they can't make money off of. The circumstances are either he makes content they use to sell their toys or he doesn't make any content at all.
The reason he potentially could continue G1 if he didn't work for LEGO anymore is that he would then have no valuable attachment to LEGO or the Bionicle IP. He would then basically be like us, just a fan producing fan content. As Eljay would aptly put it, he would be "some guy."