Hi,
Yes, if it is HD44780 compatible (which it says it is) there shouldn't be any problems, and there seem to be more/better data sheet links than normally from Ali Express. I've not checked if the pin connections are identical to the AXE133, but they should be compatible. Most controllers of that type are organised as two rows of characters starting 64 bytes apart (i.e. at addresses $80 and $C0) so the 40 characters/row shouldn't be a problem.
You might want to check the Character Set, but it doesn't seem any worse than it having a Yen Symbol in place of the Backslash. The backlight is rated at 35 - 40 mA which is more than you can control directly from a PICaxe pin, but I don't think users normally drive it like that anyway. I would expect the PICaxe/AXE133 to be compatible with 3.3 or 5 volt versions. Don't forget that you normally need a "Contrast Control" for LCD display types, but Rev Ed still appear to be selling the AXE133 (which has one).
Cheers, Alan.
