Do I need a termination letter for a tenant leaving a lease early?

[Nick Roth]

I have a situation where a tenant is backing out of the lease due to health related issues. They had signed a lease and as they was moving in, found out the home just isn't right for them. I have since then found a new tenant and had them sign a lease. 

Should I write up a termination letter to officially cancel the first tenant who ended up backing out of the property?

I would imagine I could just write a letter and have us both sign it? I would simply put in the letter - "As of January 28, 2023 both (landlord/myself) and (tenants name) are terminating the lease at (my rental address), effective immediately on January 28, 2023."

Is this all I need to do? or should a termination letter be more in depth, if necessary at all

Thanks in advance! This is my first rental and situation like this