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No, completely different disease. HIV doesn’t generate much response from the human immune system. In the cases where humans do produce antibodies, those antibodies aren’t particularly effective against HIV. And HIV is incredibly good at hiding from the immune system for however long it pleases.
Vaccines work by giving the immune system a sneak peek at a new pathogen so it can prepare defenses ahead of time and overwhelm that pathogen whenever it encounters it. But with HIV, the immune system doesn’t care when you show it the pathogen. It largely ignores it in vaccine form and it largely ignores it when the pathogen is encountered in the wild.