Pick the right cut-over date
The cleanest switch is at the start of a VAT period, after the previous return has been filed. For a client on calendar quarters, moving on 1 January or 1 April means the old system holds complete periods and the new one starts fresh. Mid-quarter moves are possible, but your reviewer then has to combine two systems for one VAT 201.
Leave the old system available in read-only form, or keep full exports, for as long as the client needs to retain its records. The FTA can ask for historical documents, and they should be easy to find.