depends on how the shop manage the procedures between the shop n custom.
if they hv prob wif them then it might take times.
however, as wat AD said, normally they wil provide u the form and receipt of ur engine once u pay for it.
last time i did my conversion and i waited for a week bcoz the engine was fresh from kontena n haven really settle wif the custom.
anyway try to "chase" them for it if not u can't hv ur engine registered