Where Moldova stands
Moldova joined the Hague Apostille Convention in 2007, and the corridor has been a single stage ever since. Document legalisation for Moldova means one certificate from the FCDO Legalisation Office, with no consulate behind it and no second fee to plan around. That settled position is good news for the schedule, but it also removes the later checkpoints that a longer road accidentally provides. What you send is what arrives, marked.
First: name the document exactly
An apostille for Moldova is added to the sheet presented, and it makes no comment on whether that sheet answers the request behind it. So the first task is unglamorous: go back to whoever asked, read the wording, and identify the precise record, rather than the one that is nearest to hand. Requests that name a category instead of a document are the usual source of trouble, and the cost of guessing wrong is a full repeat run.
Second: choose the copy that travels
Where the record is a birth, marriage or death entry, the register in Southampton can produce a fresh certified copy, and that is the sheet which should make the trip. An apostille issued in Southampton for use in Moldova is not attached to your household paper unless you choose to send it. Private papers with no register behind them are different: there the version you hold is the version that travels, so its safe return is part of the plan.
Third: settle where it comes back to
An apostille from United Kingdom to Moldova is issued by post, from an office with no public counter, which makes the return address a real decision rather than a form field. Choose one that will still be yours in a few weeks and where a parcel will not sit unattended. The charge is £45 / document by standard post, or £40 / document on the next-day service for registered businesses, and it lands on each sheet you send.