A man's paternal uncle marrying his maternal half-sister
Is it permissible for a man to give his maternal sister in marriage to his paternal uncle?
It is permissible for your paternal uncle to marry your maternal sister, as he is an Ajnaby (a man lawful for the woman to marry) to her. Allah (Exalted be He) says, after mentioning the women that a man is forbidden from marrying:
All others are lawful
However, you have no role as a Waliy (a legally accountable person acting for a woman regarding marriage) over her in the marriage contract. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.