Brain-Teaser 204: Logical will

From The Sunday Times, 21st March 1965 [link]

Uncle George occasionally wasted time on Brain-teasers, and it was expected that his will would take an awkward form. But his five nephews were surprised to learn, after his death, that he had dictated his will to a solicitor who had no use for punctuation. The will ran as follows:

maurice is not to sing at my funeral service if stephen receives the envelope containing three thousand pounds alec is to have five thousand pounds if thomas receives less than maurice alec is to have exactly twice what nigel has if thomas does not receive the envelope containing a thousand pounds stephen is to have exactly four thousand pounds

The nephews were confident that Uncle George always uttered complete sentences, none of which contained more than one conditional clause. They also felt sure that what he had said to the solicitor allowed one way, and one way only, of distributing the five envelopes (containing £5000, £4000, £3000, £2000, and £1000), which Uncle George had left for them.

Who receives each envelope? And may Maurice sing at the funeral service?

This puzzle was included in the book Sunday Times Brain Teasers (1974, edited by Ronald Postill).