Is giving money to a brother who lives in a non-Islamic country and suffers from financial and behavioral problems, and refuses to return to a Muslim country, considered aiding him in sin, or does it fall under the category of charity and helping in good deeds?

If the brother is unable to practice his religion in the lands of the disbelievers, then emigration from there is obligatory upon him. If he is able to practice his religion, then it is permissible for him to stay, even though emigration to Muslim lands is better.

One should consider the predominant benefit. If your refusal to give him money will lead to his return to Muslim lands, and that is better for him, then withhold payment, because religious interests take precedence.

However, if he will not leave the lands of the disbelievers in any case, and your charity to him will endear him, then there is no objection to spending money on him as charity, and you will be rewarded for it, while striving to advise and teach him, and help him pay off his debt as long as he is not disobedient with this debt or has repented from it.