I actually started answering your question the other day and then got pulled away. I researched as much as I could and the phone number didn't belong to anyone that I could find.
AMG, however, could very likely be a payday loan company. It goes by a bunch of different names and has been sued before for charging three-times more than the original loan amount. If your mom has had any involvement with a payday loan company at all, I would venture to guess that was them. However, when you think something is fraudulent, you should always report it to your bank. I've had similar things happen before, and although the bank won't tell me anything about the entity that charged me, they've always removed the charge.
There is a company called AMG that does digital marking. If you were doing research, you could have inadvertently found them, but I don't think they're the culprit. Digital marketers help businesses get leads online, through websites, ads, SEO, and stuff.
Direct marketing is different. This is what it's called when a company markets its products directly to a consumer. For example, if you get a postcard in the mail from a local dentist offering you a deal to come in, that's called direct mail marketing.
There is an AMG that does direct marketing and it sometimes shows up in complaint boards in the UK. This maybe could also be your culprit, but there aren't any references to them being in the US at all. That particular company apparently handles some marketing and billing aspects for a number of online companies. Now, I cannot find the company online at all, so I'm going based on consumer complaints, but from what I can surmise, they do something called lead generation- that means they put up enticing offers online, and when people call or go through the process online, the company processes the order for products or services. Some of the complaints involve free trials with auto-billing after, and at least one person said they were asked for credit card information to "verify their age," but the card was subsequently charged.
If you want to get down to the bottom of it more, you should probably have a talk with your mom about any products or services she ordered or tried online in the past couple months or whether she may have done a payday loan. Your mom probably won't know the name AMG, but hopefully you can jog her memory about other businesses she might have tried that might operate under the name. There is, of course, some possibility she never initiated any kind of contact with the company or any of its affiliates, but that's usually not the case. Best of luck to you.