A scion of a famous rabbinic family, Abraham Gershon is a descendant (possibly the grandson) of Shabsai Cohen ("the ShACh") (1625–1663).
According to the early Chasidic work Shivchei haBesht, his father gave his blessing of marriage for his sister Chana to the Baal Shem Tov on his deathbed.
But once Ephraim died, Abraham Gershon was unaware of this secret betrothal until the Baal Shem Tov revealed the engagement contract.
Abraham Gershon is probably responsible for kicking the Baal Shem Tov out of the Brody area where he ultimately settled in Medzhybizh.
[1] Affiliated with new Hasidic thoughts as well as traditional Lurian liturgy, the Baal Shem Tov entrusted his brother-in-law with the education of his only son, Tzvi.