Can they itemise the full list of expenses with some sort of proof for pricing - maybe a price list from the vendor?
It should be possible to get other committee members to vouch for the goods provided - it may have been minuted which would help.
I think that you would need either the committee and/or the trustee's to sign off the expense as a special item due to the lost paperwork, it is then down to them if that feel the money claimed was spent reasonably (not saying it wasn't - but a certain amount of back covering needs to be done to justify the spending).
As long as the expense was in line with the expectation for the event in question, it should be possible to get a written statement of spending signed off so the person can be reimburst - but also, the committee should look to have a limit on what can be reclaimed in such circumstances so that everyone knows the financial risks they may be taking. School charities being essentially run by volunteers (school parents/carers) the niceties of 'no paperwork = no claim' may be lost on some.
If the expense was NOT in line with expectations then the committee need to know that and ask questions, so again, referring the whole matter back to them for verification makes sense.
I'm sorry for the person who is out of pocket, but can't they do a little hunting and find some of the paperwork?