Full URL not showing on a forwarded domain?

Hey guys
Wondering if you can help me.
I’m creating a website for my girlfriend, and origionally we bought https://www.samakeup.co.uk, and purchased the web hosting with that domain.

Yesterday we bought https://www.facedwithbeauty.co.uk which will be the new domain name, and this is currently being forwarded to https://www.samakeup.co.uk as thats where the file directory is.

On https://www.samakeup.co.uk, I have the permalink structure so that the pages are https://www.samakeup.co.uk/contact for example, but when we view the page THROUGH https://www.facedwithbeauty.co.uk, we can’t see the full URL, which is a huge issue to us as I believe is not good for SEO?

Any help would be appreciated, massively.

Kind regards,
Matt