Tolkien never specifies, but if Frodo bequeathed them to anyone, it was probably Sam
We know that (unlike some of his other clothing which was kept as relics of Gondor), Frodo still kept the cloak and brooch after the War of the Ring was over.
Frodo and Sam, however, went back to ordinary attire, except that when there was need they both wore long grey cloaks, finely woven and clasped at the throat with beautiful brooches; and Mr. Frodo wore always a white jewel on a chain that he often would finger.
The Lord of the Rings - Book VI, Chapter 9 - "The Grey Havens"
Frodo gives over his keys and papers to Sam before he leaves, and we are not told of any exclusions from this.
In the next day or two Frodo went through his papers and his writings with Sam, and he handed over his keys.
The Lord of the Rings - Book VI, Chapter 9 - "The Grey Havens"
Tolkien never says if Frodo took his cloak with him or not to Tol Eressëa, and no specific mention of its fate can be found in any of Tolkien's known writings. But if he didn't take it with him, it would seem that it would be a fair assumption that it went to Sam together with the rest of Frodo's possessions.