Is it permissible to boycott a husband who fabricates lies and problems and refuses the help offered to him, knowing that his salary is sufficient for him? And what is the ruling of Sharia on this?

In-law relationships are significant, and good companionship should prevail among in-laws, meaning that kindness should be met with kindness. If what was mentioned about the man is true, then it is ugly of him to return your kindness with ill-treatment, unlike people of religion and generosity. It is permissible to boycott him and withhold charity from him if you are being harmed by him, but it is better not to do so unless you hope it will deter him from his bad behavior. Patience with the harm of an offender and continuing to show kindness to him may be a cause for his reform, and "Nor can a good deed and a bad deed be equal. Repel [evil] with that which is better; then verily he, between whom and you was enmity, (will become) as though he was a close friend."