If you are the lighter in shul by mincha, you say all brachos in shul. When you go home, you will not say shehecheyanu unless you are saying it for others.

If you lit at home and said all of the brachos, you still say all of the brachos when lighting in shul later, including shehecheyanu.

Stand by for a link to the shaarei teshuva.

Shaarei Teshuva 671:11 says:

If you are the lighter in shul by mincha, you say all brachos in shul. When you go home, you will not say shehecheyanu unless you are saying it for others.

If you lit at home and said all of the brachos, you still say all of the brachos when lighting in shul later, including shehecheyanu.

I think the reasoning is that each new minyan is a new obligation, even if everyone in the minyan already lit individually. I tried looking up the zera emes, but couldn't find a teshuva on chanuka. I am unfamiliar with the roshei teivos for the sefer that quotes him. In a cleaner copy of my Shulchan Aruch it looks like mem-ches-beis. Anyone?