I have synchronized the Moodle app with related website following the documentation and all works fine. But now, my university wants that I migrate from Ionic framework to NativeScript framework.
The Moodle app is developed using the ionic framework, which itself is developed on top of Angular and Cordova.
Are you talking about an app you have written youself, or the official moodle app with customisations/plugins?
If its your own app, you can use whatever framework you like for the client side code, as long as you can call Moodle's web services.
If you're talking about the offical Moodle app, I wouldn't reccomend trying to migrate it to a different framework - you'd have to rewrite at least the whole view layer yourself, and then you'll be stuck maintaining it as the underlying app is developed since the HQ team will still be developing with ionic. If you have development time to dedicate to the app I expect there are improvements you could make that would benefit the whole community