Fully understood (no refactoring). I think this should work for you:
Let’s assume your “game.lua” module looks something like this (or can be adapted similarly):
[lua]
–game.lua
local M = {}
local group = display.newGroup()
print( group )
M.group = group
return M
[/lua]
And you require it like normal:
[lua]
–ship.lua
local gameModule = require( “game” )
[/lua]
The following should get the group ID:
[lua]
print( package.loaded[“game”].group )
[/lua]
Give that a test and see if the IDs match. I had to tweak and assemble this from some project code I had on the side, so hopefully I didn’t type anything wrong. 
Brent