Is it permissible to spend Zakat money to invite a friend for Umrah with the intention of his reform and drawing him closer to Islam, and does this fall under the category of Da'wah (inviting to Islam)?

Allah has specified eight categories for the disbursement of zakat (definition), and it is not permissible to exceed them. These are mentioned in His Almighty's saying: "Indeed, [prescribed] charitable donations are only to be given to the poor and the needy, and to those who work on [collecting] them, and to those whose hearts are to be reconciled, and to [free] captives, and to those in debt, and for the cause of Allah , and to the stranded traveler; [this is] an obligation from Allah. And Allah is Knowing and Wise." Therefore, spending zakat or a portion of it on Hajj or Umrah (definition) for an individual does not absolve one of the zakat obligation, because it has been spent in a manner other than its legitimate prescribed use. As for inviting friends and others to Umrah and encouraging them towards Islam, and spending money on that from sources other than zakat, this is a good deed that falls under the category of calling to good.