You can just copy cross the /etc/letsencrypt directory. Make sure to preserve permissions and also transfer securely as you’re copying the encryption private keys.
Secure transfer can involve sftp/scp, password-protected zip or 7z files, etc.
If you don’t want the hassle or the certificates are close to expiring, you can always start over from scratch. Be aware of the rate limits, if you’ve recently requested the certificates on your current server.
Edit: As mentioned by @schoen below, if you do use 7zip/zip encryption, use a long and random password. 40 characters with symbols, numbers, and upper and lower characters is a good start. SSH is the better option, but anything is better than nothing. The less systems involved in moving the data, the better. You’re transferring sensitive material, so remember that paranoia is a very good quality.