Minor nitpick to avoid confusion: The USS La Jolla, SSN-701, does indeed have an SDV back fit to it. It is a fast attack, Los Angeles class SSN, not an SSGN. FWIW the SSGN’s were converted well after La Jolla was docked as a trainer.
The early part of my response to Lone Palm had to do with the group of Dry Deck Sheltered subs, a subject he introduced, including SSGN's. Only thereafter did I mean to pivot to the specific, older, Los Angeles class SSN-701.
I believe the La Jolla has been completely decommissioned after spending its last years as a trainer (including foreign military personnel), which was its configuration, typical use and and mission on 12/13/2013 for the hoaxed event I mentioned earlier. It was decommissioned in November of 2019.
No other vessel than an SDV was noted in the area, yet we have pictures of a zodiac, divers, an inflatable collar at the submerged engine, and a heavy, painted-brightly-orange, extensible object atop the starboard wing (upper left of image below) that all bespeak naval gear, and definitely were not part of the aircraft's manifest.