I suggest that if you want an answer on here you need to get the full story - facts and figures - from your friend and then post them on here. A far better strategy, though, as we don't know all the details, is for your friend to ring her scheme and HMRC for an explanation.
Have you had chance to consider the points I raised earlier? In particular it would help to know her marginal tax rate at the time tax relief was given, what NI was given, did the employer also contribute, what are the figures that she says amount to 40%. Also what reason has been given in this demand for another 20%. Who says it's 20%- your friend or HMRC. And are you sure it's not just 20% tax on the fund interest (rather than on the whole capital sum)?
Also please can you clarify what an unauthorised payment is