Use Letsencrypt certificates on other machines

Hi all,
I have an Hassio RPI4 with my duckdns https public url.
Everything has always worked fine but I’ve also added a new RPI4 with an Nginx server that expose other services.

HA uses port 443 and the certificate renew is ok.
The second RPI4 has to use different ports and up to now, I used HTTP port 80 for separate cert renew.
Now my new provider modem doesn’t allow NAT on port 80 so here’s my idea: to use the certificates renewed by HA.

On my services RPI, I’ve tryed scp copying the two file fullchain.pem and privkey.pem and editing the sym link (created by certbot) to point to those new files.
It seems to work but the cert info I can see from the browser are still different from the one I see on HA page, so I think the cert used by Nginx is still not the one copied from HA.

Is there anything I’m doing wrong?