How does betraying Boxer benefit Napoleon?
Boxer is by far the strongest of the animals on the farm, and only Boxer is able to hold back Napoleon's pack of hounds. Following the Battle of the Cowshed, Napoleon and Squealer tried to paint the outcome as a great victory, but Boxer pointed out that "they have destroyed the windmill. And we had worked on it for two years!" When Squealer claims that they would build "six windmills" and that the farm was theirs again, Boxer replied that they had only "won back what we had before." Boxer's display of disunity was worrisome to Napoleon, and he knew that with the powerful horse out of the way, no one would be strong enough to oppose him. By allowing Boxer to weaken himself on his split heal, his early death would eliminate any opposition to Napoleon. Additionally, by selling Boxer to the "Glue Boiler," Napoleon can gain added income and then further unite the animals by honoring their old friend's memory.
You can say that Boxer's death and betrayal help Napoleon in ways that are both tangible and intangible.
In terms of tangible stuff, Napoleon gets money when Boxer dies. He is able to sell Boxer's body to the slaughterhouse and get money that way.
As far as intangibles, Napoleon is able to use Boxer's death to his benefit. He makes Boxer something of a martyr and uses his death to inspire the others. he does this by telling the others that they should emulate Boxer -- they should take his mottoes (I will work harder; Napoleon is always right) for their own.
The last paragraph of chapter 9 reports,
On the day appointed for the banquet, a grocer's van drove up from Willingdon and delivered a large wooden crate at the farmhouse. That night there was the sound of uproarious singing, which was followed by what sounded like a violent quarrel and ended at about eleven with a tremendous crash of glass.
I think this wooden crate arrives as obviously a bunch of booze. The money made from Boxer turned into Napoleon's new hobby: drinking. The evidence lies in the actions listed in the quote above.