Welcome to BLF!
Guessing it’s a knockoff “Cree” of some kind. Can you desolder the emitter to get a look at the pad layout? I can’t tell if that lettering on the board says “3535C1” or not, but my first guess is that it’s a typical 3535 die size (3.5mm x 3.5mm for the square), in which case it’s probably compatible with all of the Cree XPL/XPE/SST20 types. Need to determine that first and then the world is your oyster and you can likely get a more efficient emitter that may bump light output a little, and you can choose your color temp and if you want a high-CRI version.
Are you positive the emitter is actually dead? The way those wire leads are bare, it looks like they could easily short out, so maybe so. You can easily test for this by applying 2-3 volts to the lead contacts (using a multimeter with a good diode test function or a battery/two batteries and some wires). Is there a electronic driver board anywhere, or is it just using that resistor by itself to control current? At any rate, probably a good idea to replace those wires or at least put some heat shrink on them so they can’t short on each other.
If you already have soldering skills and don’t need to buy stuff other than the emitter, you can probably fix this in fifteen minutes for just a few pounds if you can find an emitter locally. Ordering from China it’ll just cost a little more and you’ll have to wait awhile for it to arrive. Surely other good mail order options closer to home (Led4Power being a good one in Croatia). If you haven’t soldered before or reflowed an emitter then you can definitely still do this, but you’ll have to learn and spend a little on materials/tools. Some computer/phone repair shops will do this for you, too.
Here are a couple of stickied threads in the DIY section that you might want to look at:
Identifying emitters by photos (can mouse over the frames for different views and size comparisons): LEDs & Other Stuff - (Reference Guide)
Simple emitter reflowing method: How to reflow solder an LED emitter on a PCB or MCPCB.