@ yossi z,
The Rebbe Reb Moshe had 2 sons, Reb Avrohom and Reb Pinchas Dovid (Reb Pinya). Reb Pinya had a yeshiva in the building on 49th street but ended up moving to Flatbush (J & E29th area) where he relocated his yeshiva and opened a bais medresh.
Back to Boro Park …. Reb Avrohom moved to Beit Shemesh to try and start a k’hilla there while also spending time in BP. His son Reb Yankel opened a Bostoner Bais Medresh in Lawrence and his son Reb Yona stayed in BP under no official title.
Unfortunately the Rebbe’s health is not the greatest so he ended up staying more in EY which left the BP mispalelim without a rebbe or rov. They ended up asking Reb Avrohom if his son Reb Yona (a major talmid chochom!!) could serve as Rov, which he approved and he serves in that capacity currently.
Now it gets dicey…. When the Alta Rebitzen was nifteres about 3 or so years ago, one thing lead to another and the building was sold right out from under the Boro Park k’hilla. B”H they were able to find room in the Novominsk basement (16 ave & 47st) where they are today.
The older mispalelim look at Reb Yona as an extension of his grandfather Reb Moshe ZTL. The way he speaks in learning and interacts with people is quite reminiscent of his Zayda ZTL.
I hope that helped.