https://en.wikipedia.org/wiki/Carrier-grade_NAT#Disadvantages
May give you a basic understanding of what I mean.
It's normally more of an issue for hosting a service than connecting.
I'd have a guess the device with the issue will be Telefonica carrier.
Service provider blocking ports? Are you all with the same provider?
You have proved the devices and the account settings if it works on LAN so the only thing I would say is left would be a service provider issue.
As I said its an account thing, humour me, get him to connect to his own DVR using someone else's account login. Preferably one that has proven to work on 4g