Yes, SARS-CoV-2 Coronavirus infection can induce permanent immunity after recovery if a healthy person produces a number of antibodies that successfully neutralize the virus after infection. In addition, the second important issue is the answer to the question: Will there be other, equally dangerous, new versions of the SARS-CoV-2 Coronavirus causing Covid-19 in the years to come after mutations? We currently don't know the answer to this question.
As evidenced by the latest research, the immunity to COVID-19 after recovery is very soft, and not solid.
In the same vein, no hope of durable COVID-19 vaccine, no immunity passport, and convalescent plasma works in some other way if it works at all. Seconf infections can also occur.