Group them just before the move.
When you're ready to change sheets, hold <Ctrl> and click on the tab of the
sheet you're going to work on next.
Release <Ctrl> and click in that sheet tab again and you'll be in that new
sheet with the focus on the cell you were in on the first sheet.
You now have to "break" the grouping (ungroup) before you can work in the
new sheet.
Right click in the sheet tab and choose "Ungroup".
NOW, this sounds kind of complicated with a lot of superfluous motions, but
I use this procedure, and once you become accustomed to what you're doing,
it's really fast and simple, considering 3 of the 4 clicks is in exactly the
same place, the new sheet tab, and the fourth is in the pop-up menu, right
next to that sheet tab.
<Ctrl> <Click> - <Click> - <Right Click> - <Click>