SIM cards are provider specific, even between a parent provider and one of their subsidiary brands. If you have a Public Mobile SIM and are switching to Telus, you’ll need a Telus SIM card. SIM cards do expire if not used for I believe it is 45 days.
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I don't think SIM cards expire. I've used spare new SIM cards that I've had lying around for more than a year. Once registered they can't be reused for another account even if was unregistered from the first account.