Is it permissible to issue a document stating that the questioner is the sole provider for his mother, knowing that he is not, in order to enable her to receive medical treatment at the expense of the Cultural Attaché?

If you do not spend on the house and your mother, you are not considered her provider, and it is not permissible for you to present a deed to that effect, as it involves lying, deceit, and consuming wealth unjustly. You must seek a lawful way to treat your mother.