Sims 3 Imaginary friends

@elimaximoff  The imaginary friend shouldn't disappear.  But in practice, it might depend on the way your sims move towns.  The EA method of using the phone to move is unreliable in a few different ways and often doesn't work as intended.  Without mods, the best way to move is to save your sims to the library, save their household separately if you want to keep it, quit to desktop and reload the game, start a new save, and place the bin copy of your sims in that new town.

I'd suggest trying this just to see what happens, and if you don't like the results, you can try a different approach.  If you use mods or are willing to try them, you'll have more options as well.