Bishop Sophronios/Sophronius (Beshara) was a bishop for the Holy Eastern Orthodox Catholic and Apostolic Church of North America (HEOCACNA), an enterprise started by Bishop Aftimios.  For all intents and purposes, the jurisdictional unity attempt died in 1933.  Bishop Sophronius, however, was the last bishop.  The date of his death has been given as 1934 by Archimandrite Seraphim (Surrency) in his book The Quest for Orthodox Unity in America.  Others have often followed that.  Yet, his grave marker states 1940, a date noted here as well:

http://meta.orthodoxwiki.org/Sophronios_%28Beshara%29_of_Los_Angeles

This begs the question of which is correct and if 1940 is correct, what was he doing during those intervening years?

Well, 1940 is correct and what he was doing was ordaining people to his American Orthodox Catholic Church (an alternative name for HEOCACNA).

Here are two examples of newspaper articles referring to him ordaining men to the priesthood:

1939 Sophronios Ordains a Priest

Sophronios Visits Binghampton 1939

For those interested in the beginning of his episcopal career, these might be of interest:

Sophronios to be Elevated

Sophronios Ordained 1928

Purpose of HEOCACNA and Sophronios