At this address, you will find a complement written by Vincent Presumey on the trade-union work of Lambert, reviewing the 1940s, the 50s, and then the entry in FO in 1961/62.
There is one mistake rectified by Vincent about Lambert: he was expelled from the CGT at the begining of the 50s but succeeded to getting reintegrated by Benoit Frachon himself in 1954 and even managed to have one office in the CGT and one office in FO !!!
The combination between Lambert and Bergeron started at the 1959 congress of FO. Lambert fully integrated FO only in 1961, but the original deal between Lambert-Hebert and Bergeron is dated from that 1959 congress.
The source is an academic thesis written by Jean Hentzgen, who helped Vincent to establish the historical truth hidden behind the smoke of the Lambertist mythology.