To do this is relatively simple since your application works as expected and you just want to add a novelty/function.
The first thing to be considered is to create a service to run in the background, there are several plugins to facilitate this process. You can check the following:
https://github.com/katzer/cordova-plugin-background-mode
https://github.com/Red-Folder/Cordova-Plugin-BackgroundService
With a service in the background you should wait (or listen) the event online
Cordova. It will be issued as soon as the device connects to the Internet. More information on how to do this at this link Cordova Online Event.
When the user registers and has no internet connection you must store the information or even the request in the device. As soon as the event online
If triggered you check what information is saved to be registered and try to register. However it is valid to inform that if any given is not correct you will have to treat them differently, perhaps with some notification.
To save the data on the device you can use various technologies, see that one response to get a better view.
Okay, I get it but I need it to work in the style of "Dropbox", even if you close or minimize the application on the phone it still sends the data, has how to do this?
– Vinicius VAz