In the TV show Only Fools and Horses a character called Trigger has a sweeping brush. He is proud that he has had the same brush for 17 years. However he reveals he's replaced both the head and handles many times over the years (hint: humour). In other words, though the object to him remains the same object, every part of it has been substituted many times.
It seems to me that there ought to be a word or phrase to describe this concept in philosophy, because it goes to the heart of the problem of identity of all objects both inanimate and animate.
What is that word or term?