Owning two homes for a short period of time - CGT?

I have lived continuously in my current property for 8 years. I am in the process of purchasing a new property, which will then become my primary residence, and have the funds to do so before I sell my current property. Whilst I would have liked the sale/purchase to tie up, that is no longer going to happen. It appears as if my purchase will go through in January, but my current property sale may be later in the year, lets say April/May. For this period of time I will effectively own two properties. I've been reading up and I believe that the last 9 months of ownership always qualify for full PRR (Private residence relief) so long as it was my primary residence at some point? I'm just double checking my understanding - does this mean that if it takes me 4 or 5 months to sell my house after it is no longer my main residence, then no CGT is due as full PRR applies? If so, I'm assuming I need to notify HMRC of my primary residence updating when I move to my new house?

Hi,
You can see the following guidance regarding the right of nomination of your main residence:
CG64485 - Private residence relief: only or main residence: two or more residences: right of nomination
Private Residence Relief can be applied against your main residence. You can see information here:
HS283 Private Residence Relief (2024)
Thank you.