Hi AlexRus,
I am not sure with your data source. Say you are using Excel table as your data source.
I create an Excel table looks like below, the table name is table8.

My steps:
1. Create a connection from PowerApps to data source. Add two screens. On my side, they are Screen2 and Screen3.
2. On screen2, add a Gallery control, set its Items property as table8, show students name on the gallery.
3. On screen2, add a DisplayFrom control, set its Data source as table8, Item property as Gallery1.Selected. Then add an Edit Button control and set its OnSelect property as EditForm(Form2);Navigate(Screen3,ScreenTransition.Fade)

4. On screen3, add an EditForm control, set its data source as table8, Item property as Gallery1.Selected. Then add a Submit button control and set its OnSelect property as SubmitForm(Form2);Back().

Hope my steps could be a reference for you. If you need more help, please feel free reply.
Best regards,
Mabel Mao