I'm not sure whether the term "separation agreement" in the quote from Pub. 523 would include an informal agreement. If that's your situation, I suggest that you consult a local tax professional for guidance. Your original question stated that the couple was "already divorced" and referred to the "ex-spouse."
Note that an informal separation, without any kind of court order, is a totally different situation. In that situation you are still married. You have to file your tax return as either married filing jointly or married filing separately (unless you meet the requirements to be "considered unmarried" for purposes of filing as head of household).
