A father and his late son have lost an appeal against their convictions for the theft of greenstone (pounamu) from Ngai Tahu.

David Saxton, 62, and his son Morgan Saxton, 30 were found guilty in 2007 of the theft of hundreds of thousands of dollars worth of pounamu from South Westland's Cascade Plateau.

David Saxton was sentenced to two years and nine months imprisonment and his son to two years and six months jail.

They were also required to pay reparations of $300,000.

The pair launched an appeal against the convictions and sentence last year, but before the case was heard Morgan Saxton was killed in a helicopter crash in Wanaka in November.

However, the Court of Appeal allowed his mother, who was granted control of her son's estate, to continue the appeal.

In a decision released today the court dismissed both men's appeals against conviction, but granted David Saxton's appeal against his sentence.

The court quashed his original jail sentence and replaced it with six months' home detention.

Morgan Saxton's appeal against sentence was dismissed.