AddOns need to save the data as SavedVariables in your folder live/SavedVariables.
Read here how to find the addons folder. It's live/AddOns, so you are able to find live/SavedVariables easily:
https://www.esoui.com/forums/faq.php..._howto_install
And these mobile apps most likely depend on an addon which you need to install to dump the research timers to the SavedVariables, then upload the SavedVariables somehow to the app.
I bet the app explains what is to do where in it's description at the app store? Or after installing it maybe.
And if this is not supported you manually need to keep track of the changes ingame by just clicking the stuff at the same time in your app then I guess.
Maybe this addon (there also exists a windows tool for this,s aerch for igor) is a helper as well if it still works:
https://www.esoui.com/downloads/info...Assistant.html