It doesn't work in FR and LG? Drat.
And what do you mean by 'giving the stones?'
Oh I didn't know that. Is that true for all the games?
Um, forgive me if my memory fails, but after you defeat Blaine, Bill asks you to take a ferry to the new islands. You complete some side mission against Team Rocket and find a Ruby and a Sapphire. You give these stones to Celio (Bill's friend) on Knot Island and they'll fix the Network Machine. This gives you access to Johto pokemon, and this is when Suicune's values are set. If you're looking for a specific nature for Suicune, you need to save and reset here.
Synchronize does not work in: FireRed/LeafGreen, Ruby/Sapphire, and Colosseum/XD. It only works in Emerald and beyond to DPPt.
You can use Synchronize on stationary legends, such as Rayquaza or Giratina.