Is it illegal for someone in California to claim to be someone’s POA if they’re not?

thank you for your comments. the old POA is VERY aware she has been removed -she was present at the court (via video call) however she acts like the rules don't apply to her. the care facility are also aware she is no longer POA and have the relevant documentation/information for the new POA. the old POA is trying to appeal the courts decision. one of the reasons she was removed was for not paying his health insurance/care home fees. i just wanted to know if and when she instructed a doctor to come to the facility (even though the doctor was prevented from examining the charge) if she would've had to say she was his POA? i guess it's not that important as she's not doing anything 'fraudulent' however i would like the court to be aware of this so they can see she is going against the court order. the new POA is aware of the above also so she will also make it known I'm sure. many thanks for all your replies.

I would think misrepresenting one's self as POA would be a form of forgery

IF she WAS the POA, then she will still be listed as that with all banks, all stock companies, all bill companies and all MDs. The NEW POA must go to all of these entities and register as the new POA, including the care facility. This is part of your new duty as POA as is the meticulous record keeping of every penny in and every penny out for the durations, as well as keeping diaries of such instances as this.
The new POA may claim that he/she had no idea he/she had been removed as POA and there is of course nothing to prove otherwise unless she was legally served and notified.
None of this is as easy as saying "Hi, I am the POA". These things are WRITTEN in black and white. And when one things is changed then every single thing has to be changed.
Whether it was legal or not, her claim that she had no idea she no longer was MPOA and saw a need for help will likely have her excused in court this time.

You're getting into a touchy fraud area here,  i.e., someone allegedly made fraudulent representations, and apparently acted on them.

Fraud is an iffy area of law; the standards are specific but sometimes vague (even though that doesn't always make sense), and fraudulent verbal and/or written representations or conclusions shouldn't be made by anyone except an attorney qualified in the area of fraud.  

What would you consider doing if this individual actually did commit fraud?  Would you be filing a police report?  Elder abuse report?

Not sure about illegal. The problem with DPOAs, not sure if the court system has caught up with how much a DPOA can be misused. If a State allows you to download paperwork and all you need is signatures and a notary, how binding is it really. Thats why I say use a lawyer who will make sure that your rights are covered.

If #1 is aware that she is no longer DPOA, then as Geaton suggested, get a lawyer to send her a letter to cease and desist. I would also make sure anyone #1 dealt with for Mom be made aware she is no longer POA by sending them a copy of the letter revoking her. Also, maybe giving info about the new POA.

She would have had to show the document to the clinic for them to have on file. I would call that clinic to clarify she's not the PoA. Then I would have an attorney draft up a letter threatening legal action if she continues to misrepresent herself (whether it's legal or not and this could vary by state). That should be enough to scare her to stop.