assignment of 50% of the copyright to the song.
Are you joint authors of the musical work? As for the version of the song with the lyrics, you can register this as a jointly-authored work provided that each of you prepared your contribution with the intention that it
would be eventually combined (into a single song). Even if the composer didn't know you at the time of writing the instrumental, it can still qualify as a jointly authored work if the composer had always intended that words would be added. In that case, you can register the song as a jointly-authored musical composition. The law presumes that your shares are equal but its best to memorialize that arrangement with a collaboration agreement. Otherwise, confusion may occur.
If the composer did not originally intend to add lyrics ... In that case you can register the words and music as a musical composition as a derivative version of the original instrumental and list yourself as a co-owner (assuming composer assigns you a 50% ownersip interest).
P.S. Thanks for using Getting Permission, but we think Music Law might provide more help.