This song originally existed with different lyrics under the title "What Do You See In Him?". See latter link for information on that stage of the song's creation.
The "Wonderful Woman" lyrics were written in the Spring of 1983. This second incarnation was first professionally recorded on 26 June 1983 for the band's first appearance on David Jensen's BBC programme (first broadcast on 4 July 1983), with producer Dale Griffin.
The song was recorded again in July/August 1983 at London's Elephant Studios with producer Troy Tate in the sessions for the band's debut album.
The definitive version was recorded in September 1983 at Matrix Studios in London with producer John Porter.
There are 12 confirmed live performances of the song between the moment it re-emerged into the Smiths' set as "Wonderful Woman" in early June 1983 and the end of September 1983, after which it was released and heard one final time in November 1983. However, if we take into account the fact that information is missing for a good number of setlists from this early stage of the Smiths' life, the number of actual live performances can safely be assumed to be 15 or 16. The song was soundchecked on the British leg of the Meat Is Murder tour but never made the set.
There are no officially released live recordings of the song at this point in time, but bootleg recordings are circulated.