As Income Tax is levied upon a person's total income, and we don't know what other income your acquaintance has, it's impossible to provide a definitive answer here. If, for example, her income before taking her late husband's pension into account already took her into one of the higher tax bands, she'd pay a higher rate of tax on the additional income on the pension. If, though, she has very little income of her own, then much of her late husband's pension would be taxed at the basic rate.
Let's assume though she's not yet reached pension age herself and her only income is from her late husband's pension. Then she'll pay no tax on the first £12,570 of the pension income. The next £38,000 (or anything up to that amount) will be taxed at 20%. As she's paying £3,000 a year in tax, that would mean that there's £15,000 of income that's being taxed at 20%. Thus the total amount of the pension would be £12,570 + £15,000 = £27,570 per annum (= £1,838 per month).
However if your acquaintance has got sufficient independent income to take up all of her personal allowance, then (as long as her total income doesn't come to more than £50,270), she'll be paying 20% on the whole her late husband's pension. That would mean that the pension is only £15,000 per annum (= £1,250 per month).
If your acquaintance is lucky enough to have personal income exceeding £50,270, she'll be paying 40% tax on her late husband's pension. That would mean that the pension would only need to be £7500 per annum (= £625 per month) to get taxed at £250 per month.
So, as I stated at the beginning of my post, there can be no definitive answer to your question.