The animals are already working hard at the time of Boxer's death, but the pigs use his memory to try to reinforce an ethic of labor and obedience. While it's clear that the pigs sold Boxer to the glue factory and spent the earnings for a case of whiskey and a drunken revel, they make up a story that Squealer repeats. In this story, Boxer died in the hospital, having received excellent care. Napoleon purchased expensive medicines for Boxer, not for a moment thinking of the cost. The animals believe this story and are relieved to think that Boxer died happy.

Napoleon himself gives a short speech, which he ends with Boxer's two favorite maxims: "I will work harder" and "Comrade Napoleon is always right." Napoleon advises the animals that they should adopt these maxims for themselves. The pigs, knowing that Boxer was admired and influential among the animals for his hard work, sincerity, and dedication to Animalism, are trying to use his reputation to influence the animals.

The novel never says that this tactic is effective, but we do know that the animals toil in hardship at the end of the book, often hungry and cold, living in spartan conditions and no longer expecting the dreams of the rebellion, which most can't even remember, to come true.

How did the pigs use Boxer's death to get to the animals in Animal Farm?

In the end, the animals realize the painful truth about Boxer's death.  Essentially, given Boxer's strength, his loyalty to the pigs and all of the animals, and his work ethic, the animals sadly realize that if the pigs could get rid of him, they have no hope.  If Boxer is met with an end that represents how the pigs use and discard animals, then they realize that their hopes of being saves or spared are futile.  Given everything else they had experienced, Boxer's death represents the last straw of hop,e and when that is gone, the animals forfeit any chance of rebellion or seeking better treatment.  For their part, the pigs use Boxer's death as an example of the extent of their power.  The story they tell is one whereby the animals learn of the care Boxer received and then of his death.  Yet, the animals know that the pigs arranged for his death and with this, the all encompassing power of the pigs becomes apparent and evident.  In this, the pigs are able to gain a great deal of power and unquestioned control over the animals.