Hello I have the following question
Would I like to insert the resolution of app.manager.it to the IP address 192.168.1.226 internally in the DNS?
I would like 192.168.1.226 to answer me if I ping app.manager.it within my network. It's possible?
How can I do?
Sincerely,

It depends. Router can do it:
But it will only work if connected devices use only this router as DNS resolver, they must not ask another (e.g. external DoH as some web browsers do).

If it's for some service that's accesible from internet using ports forwarded to internal server, and you need the same hostname to work also from LAN, then more foolproof method is thing called "hairpin NAT", see e.g.: viewtopic.php?t=179343