started in self-employment then changed mind, advice needed

[brrapp]

Hi all, my daughter is looking for some advice.
She was in full time employment then left voluntarily a month ago. She had a few contacts so decided to set herself up as a self employed (sole trader) contractor. She did two days work for one business then three weeks for another. The one who gave her the three weeks work were impressed with her and wanted her to stay permanently so offered her a full time job with good conditions that she would be foolish to refuse. She starts next Monday in the full time position.
She hasn't even informed HMRC that she'd started as a sole trader or set up a business account yet but has had one payment from each client.
I'm not sure if she can register as a sole trader then inform them immediately that she's stopping. Would it be simpler (and legal)for her just to hand the money back to the clients and act as if she had never been self employed? I'd imagine that given the sums involved it would be worth while sacrificing them rather than going to the expense and trouble of preparing accounts for 3 weeks work, or does anyone have any alternative suggestions?

[brrapp]

Thanks, should she just hand over her p45 from her last employer to the new employer as if she hadn't done the intervening work then fill in a self assesment form for the self-employed work seperately?