Is financial assistance obligatory for someone who claims to be a refugee and in need, despite doubts about their identity and the sincerity of their claim?

You can verify her condition and truthfulness before helping her, or appoint a trusted person to deliver your charity and ascertain her situation. If you give charity to her without verification, you will still receive the reward for your charity, as narrated by Al-Bukhari from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace be upon him) said: "A man said, 'I will give charity.' So he went out with his charity and placed it in the hand of a thief. The next morning people were talking, 'He gave charity to a thief!' He said, 'O Allah, to You be praise. I will certainly give charity.' So he went out with his charity and placed it in the hand of a prostitute. The next morning people were talking, 'Tonight he gave charity to a prostitute!' He said, 'O Allah, to You be praise, for [giving charity to] a prostitute. I will certainly give charity.' So he went out with his charity and placed it in the hand of a rich man. The next morning people were talking, 'He gave charity to a rich man!' He said, 'O Allah, to You be praise, for [giving charity to] a thief, and a prostitute, and a rich man.' Then he was told, 'As for your charity to the thief, perhaps he will refrain from stealing. As for the prostitute, perhaps she will refrain from her fornication. And as for the rich man, perhaps he will take heed and spend from what Allah has given him.'" We advise you to verify her condition or give your charity to charitable organizations or to someone you trust to deliver it to the deserving.