J-2 Visa holder working remotely abroad

Hi all,

My wife will be coming to the US on a J-1 Visa, and we're planning on putting me forward for a J-2 visa as a spouse, so I could join her.

I currently work in the UK, and would like to continue to do so while in the US (a few months long visit). Am I legally allowed to keep working while in the US at my UK company remotely on a J-2 visa? I'd keep my UK residency, UK bank account, so forth. I've been trying to find information online, but can't seem to find the answer to my question.

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Anyone with similar experience around?