Inherit of Ascension Stone

I remember seeing a post about this, but I can not find it. It must be older than I thought.

I went to replace a hero and inherited the hero skills over. I had the same problem as another poster with the Element Training not inheriting the first try, but I did a second inherit and it fixed that problem. I replaced the basic gear the hero came with, with the gear from the hero I replaced and moved on. As I was checking to make sure I did not miss anything, I found that the Ascension Stone did not Inherit. I tried another Inherit but it still did not move. I tried to Inherit the weapons but the system will not let me inherit from basic gear to L3 gear. Before I pull gear from another hero to try to inherit and losing other progress on said gear, I would like to ask.

Is there a way to inherit Ascension Stone training without using other L class gear?