In that case what I would recommend is to change the issue date of the invoice but keep the tax date of the invoice the same. HMRC should be happy that they have been entered into the correct period and should work for your client as well. You might want to phone HMRC to confirm they are happy with that idea. Their number is 0300 200 3700 but be prepared for a long wait.
In terms of how you would move just the invoice date and not the tax date that might be a question for @qfsupport to answer rather than myself.
I hope that helps.
Kind regards,
Chris