Licensing and activation work differently in Windows 10. I'll explain with a metaphor:
Say you're going to a museum. You present the ticket-taker with your ticket, after which the ticket-taker stamps your hand, allowing you to enter and re-enter the museum without needing a ticket.
Your license is the ticket. Your hand stamp is the activation. The license gives you the right to be activated, and once you are activated, your activation is valid forever. You no longer need your license.
In your case, your computer has already been activated. Installing your SSD won't change that, because once your computer is activated it will always be activated. So you no longer need to enter your license.
Or as my teenager would say: You're in, bro.