This is true, although my own canonical transfer to the Melkite Church took all of two months from the time I sent off my letter to the Archbishop requesting transfer (and just in time, too, since soon after, it was announced that he’d be transfered to Lebanon, and we got a new Eparch!).
I sent a letter to the Archbishop, who asked for the consent of my Latin bishop (which was readily given). About five weeks from the time I sent my letter, my pastor received the Decree of Transfer of Ascription and an Acceptance of Transfer of Ascription, which I was to sign in the presence of two witnesses. Getting the witnesses lined up to attend a Sunday Divine Liturgy took a bit of time (especially since I was out of the country for two weeks after my pastor got the letter), but everything was done and signed less than a month from the time we received word from the Eparchy.
I hope it goes well and smoothly for you, too, ConstantineTG!