I've got a question: can I say "It fell into my memory" with the meaning of "I remembered it very well"? I know there are expressions such as "It was etched on my memory", but is the version with 'to fall into' also correct?
If I were to read that phrase, I would think it was something that you had just remembered. In other words, you've been trying to remember a name and then it "just fell into your memory". "fell into" implies an abrupt appearance, not something deeply etched.