So let me get this straight. You or your customer had their images stolen and is hosted by this company. This company wants to be your Power of Attorney, to represent you. So this company wants to represent both the company that steals images as well as the rightful owner of the images?

It sounds like a real estate agent representing both the seller and buyer, a conflict of interest. I'd be looking for a lawyer in their country.

You pretty much summed it up. I had that same thought. And this part is really weird

Purchase, test, and authenticate products that are suspected to be infringing our/my intellectual property right(s) and issue authentication report(s).

Why?

It may be a stall tactic, or one used to invalidate your legal claim. I am suspicious and would contact a lawyer in their country.

what is your opinion of this request?

Sounds like the quick answer to their request is “####, no.”

Doesn't the “power of attorney” business basically mean that you're giving them permission to decide for themselves whether any given action--including their own--constitutes infringement? Gee, I wonder what they’d decide.

Doesn't the “power of attorney” business basically mean that you're giving them permission to decide for themselves whether any given action--including their own--constitutes infringement?

As I read the document, yes. And my immediate response is no way, but it is ultimately up to the client.

Power of Attorney is a legal concept pretty much accepted world wide. You need to DENY this request (a simple NO will suffice) and indicate you have advised your attorney to look into this false claim (use those words: false claim).

Meanwhile, do a little research yourself, or chat an IP attorney in your own country as regards this "odd email I got"...

You can start legal proceedings from any country against any country ... whether it will make a difference depends on the laws of the countries (persons) making demands.

After all, if Canada, Germany, France, Spain and a few others make demands/claims against the rest of the world there's nothing that prevents you doing the same. And since this appears to be extortion of a particularly nasty kind, I'd go for it.

Meanwhile, send a DCMA against their host, cc to g b and y and go about your day.

As this point (without being rude) the barn is already on fire and all the cows have escaped. Your client's images are gone, a clever shyster is hoping to make a mint, and EVEN if you play their game, your ip (product) is already gone.

Just as you (likely) have little recourse in their country, they have little in yours. Works both ways.

I'd ignore it with a watchful eye.

As usual, this is not legal advice, as stated above, consult an attorney of YOUR choice in your country on how to either respond, or ignore, this.

is the infringing party the platform itself or users of the platform?
perhaps that distinction explains why they asked for this.

you should probably consult an IP attorney in the jurisdiction in which the platform does business and perhaps where the infringing content is hosted as well.

is the infringing party the platform itself or users of the platform?

The infringing parties are the sellers who use the platform of the company asking for the power of attorney. And the owners of the platform have the usual boiler plate T&C that the sellers are solely responsible for their content.