From "Early Rapid Transit in Brooklyn, 1878 - 1913" on this site ...
July 17th, 1898 saw the first joint service between the Brooklyn Elevated Railway and the LIRR. The Chestnut Street incline opened connecting the Broadway - Brooklyn El to the LIRR at Atlantic Avenue and Rockaway Avenue. El trains ran through to Rockaway Park. On October 4th, LIRR trains ran through service from Broadway Ferry to Jamaica using the incline. This service lasted only three months, ending January 10th, 1899.
With BRT control came electrification and through services on the Els. By July 1st, 1900, the Myrtle Ave and Lexington Ave Els were electrified, as was the Broadway - Brooklyn El between Broadway Ferry and East New York.
The LIRR electrified the Chestnut Street incline on July 28th, 1906. A special adapter at the beginning of the ramp along the LIRR's Atlantic Ave line enabled the third rail shoe of the LIRR cars to be moved to the "correct" position for traveling over the El. Service ran to Broadway Ferry until May 30th, 1909, when LIRR service was extended over the Williamsburgh Bridge to the new "Manhattan Terminal" (today's Essex Street). Service lasted until September 3rd, 1917, and the structure was not dismantled until 1942 (although parts were torn down in 1924).
--Mark