Dear Niphon, welcome to the forum. Here are two articles from Notes From the Underground that tell a little about his life.
Bp Anthony (Grabbe) Blessed With Kursk-Root Icon
(NFTU: New Jersey, 7/24/2005) From his hospital bed, Bishop Anthony (Grabbe) venerated the Wonderworking Kursk-Root Icon.
The icon was brought to the hospital by Bishop Gabriel of Manhattan (ROCOR-L) at the request of family members. Bishop Anthony is reportedly near death and is in critical condition. During his youth in Belgrade, the future Bishop Anthony would carry the icon in processions, sometimes in extremely dangerous conditions.
Archimandrite Anthony left the ROCOR Synod as an Archimandrite for the Greek Old Calendar Church in 1995 according to the official website of the ROAC, for reasons that are still hotly disputed today. He was made a Bishop in one of the Greek Old Calendar jurisdictions. In 2001, Bishop Anthony entered the ROAC as a retired Bishop.
More details concerning Bishop Anthony's health are forthcoming.
Bishop Anthony (Grabbe) Reposes in the Lord
(New York - 12.09.05) His Grace Bishop Anthony (Grabbe), son of Bishop Gregory (Grabbe) of New York, has reposed in the Lord at the age of 79. He reposed at about 11:15 AM Eastern Standard Time.
Bishop Anthony became a Bishop under one of the branches of the TOC of Greece after leaving the ROCOR in 1985. He was received as a retired Bishop of the Russian Orthodox Autonomous Church in 2001. The son of one of the most eminent canonists of the ROCOR, Bishop Gregory (Grabbe), Bishop Anthony contributed the wisdom of old Russia to our Church in its most difficult period. He was quoted as saying, when asked why he would be accepted as a retired Bishop in ROAC, "that I wish to die in the Russian Church."
According to Fr John Shaw of ROCOR, Bp Anthony will be buried at Novo-Diveeyevo Convent in Spring Valley, NY.