The Parliament website says that:
"Traditionally the Chief Whip of the political party whose MP held the vacant seat will begin the procedure for a by-election. This is known as 'moving the Writ' and takes the form of a motion in the House of Commons."
This has to occur within the next three months now that the vacancy has arisen. Now the highest level Chief whip that Sinn Féin have within the United Kingdom is Carál Ní Chuilín at the Assembly, who is not one of their 4 remaining MPs, not that she or any of the 4 MPs are likely to take the oath merely to move the writ.
The recent occurrence in Oldham East and Saddleworth was moved by the Liberal Democrats because although Phil Woolas had been elected as a Labour MP upon the initial court hearing he was suspended from his party, therefore the Lib Dems in second place were the top party in the previous election to have a party member still from that ballot.
In the case of West Belfast it may well fall upon the SDLP also the party in second place in May's elections who are the party that will move the writ as no members of the party who have vacated the seat have a member sworn in at Westminster.