I'd say, if that receipt stapled in your passport that says "have to report for 90-days on (date)" says you should report soon, then you can do this on just ANY immigration office in the country. However you COULD be asked where you currently stay, if it is not a hotel which would otherwise have registered your TM30, but a private address, you MIGHT be asked to fill a correct TM30 (which actually has nothing to do with the 90-days reporting)
90-days Non-O married to Thai, then after entry in Thailand, park the 400,000 THB and before the 90 days run out, apply for the 1-year extension based on marriage with a Thai . .with this extension he can leave and re-enter Thailand as he wishes, he only needs to buy a re-entry permit for each trip
so if you show up on March 20, they will probably add 60 more days from that date (not from 13th of April) but different Immigrations have different ways. You will need everything document wise what you also needed for the previous 60 day covid extension
you should thank them for pointing out that you can get 60 more days by just showing up before the March 30 deadline for Covid-extensions. If you wait until 13th of April, and they discontinue the Covid-scheme extension, you would be left without the possibility to extend again
some Immigration will want him to apply for the 30 days extension first, before they issue a 60-days covid19-extension. Some will give him the 60-days covid-extension right away, skipping the "normal" 30 days extension. Be aware the covid19-extension will start from the day he applies, while the 30-days extensions will be granted on top of the current end of admitted stay
he "used" the visa for entry by December, I can see a number "5". . .which could be his entry date, the 5th, the 15th or the 25th. When did he enter Thailand ?