The Invisible Boy (1957) is sort of a sequel and/or a prequel to The Forbidden Planet (1956). Due to time travel it is sort of a prequel, happening centuries earlier, and sort of a sequel, happening later in the time frame of Robby the Robot.
Thus if there are ever a series of The Forbidden Planet movies, or Robby the Robot movies, or Commander Adams movies, or Forbidden Planet space force movies, etc., or a television series on any of those subjects, The Invisible Boy could be watched either before The Forbidden Planet, and possibly as the first in the series, and/or after The Forbidden Planet, and possibly the last in the series.
Of course there are some purists who might claim that there is no 100 percent certain proof that The Forbidden Planet and The Invisible Boy are in the same series, but there are probably millions of people who believe that those two movies are part of the same series.
As K-H-W says in his answer there is a stage play Return to the Forbidden Planet which is said to be a sequel, though how people can return to an exploded planet is beyond me.
And as Buzz said in his answer there is a novelization of The Forbidden Planet written by Philip MacDonald under the name of W.J. Stuart.
And a number of people have tried to make remakes, reboots, sequels, and prequels of The Forbidden Planet, and there could have been story outlines and scripts written for such projects which someone might be able to read somewhere.
And as far as I know that is just about everything that exists in the same fictional universe as The Forbidden Planet (1956) at the present time.
A lot of the props from The Forbidden Planet (1956) were used in other science fiction and fantasy productions.
The original Robby the Robot costume has been used in many movies and television episodes, as have copies of it.
I believe that Forbidden Planet uniforms have been reused in other movies and TV shows.
I believe that the "Amazon Women on the Moon" segment of Amazon Women on the Moon (1987) featured uniforms based on those in The Forbidden Planet (1956).
Some scenes in the time tunnel complex in The Time Tunnel (1966-1967) seem inspired by the Krell Machine, as dose the Great Machine on Epsilon 3 in Babylon 5 (1993-1998).
The Star Trek episodes most like The Forbidden Planet (1956) to me include "The Cage" (1964), "The Menagerie" (1966), and "Requiem for Methuselah" (1968).
The Wizard of Mars (1965) may seem to some like a mixture of The Wizard of OZ (1939) and The Forbidden Planet (1956).