1956: NYCTA subway service is extended to Southwest Queens and the Rockaway Peninsula with the opening of service between Rockaway Blvd. Station, and Rockaway Park and Wavecrest on the Rockaway Peninsula. The old LIRR route across Jamaica Bay was repurposed for the subway. A May 1950 fire burned out over a thousand feet of the cross-bay trestle and was the catalyst for NYC to purchase the line from the LIRR in 1952. Rebuilt for subway service, the link opened June 28, 1956. The final station on the east leg, Far Rockaway, did not open until January 1958 in order to permit construction of a new terminal station; thus Wavecrest was the east terminal for a year and a half.
Fast forward to 2012. Superstorm Sandy badly damaged the 1956 cross bay trestle, so once again service was suspended till the current trestle opened.
I have often wondered why the subway service was terminated at Mott Ave instead of at the city line. A new Far Rock terminal could have been built within both city limits and the LIRR inwood station just across the line in Nassau County.
One thing that might be interesting to know is how many people transfer between the LIRR at Far Rockaway and the A at Mott Avenue. It's only a few minutes' walk from one to the other. This transfer might make sense for people who live in Arverne or Edgemere and work in the Penn Station/Atlantic Terminal area.
Mott Ave is in a commercial area with shops and services, and was the location of the original LIR Far Rockaway Station. Bus routes serve the location as well. Plus LIRR needed a location for its relocated Far Rockaway Station at Nameoke Street because there is small yard immediately west (operationally, that is) for storing two trains.
Even without the existence of an MTA as we know it an NYCTA facility could have been built across the street from an LIRR one independent of each other but close enough for passengers to transfer if necessary.