Where neither kasrah nor an unvowelled yāʾ precedes the pronoun, the book generally assigns ḍammah. Its examples include لَهُ، رَسُولُهُ، مِنْهُ، أَخَاهُ، رَأَيْتُمُوهُ.
In مِنْهُ, the preceding nūn is sākin, not yāʾ. In رَسُولُهُ, the preceding lām has ḍammah. Both therefore have هُ.
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Ordinary ḍammah elsewhere
Rules of Hāʾ al-Ḍamīr: Vowels, Ṣilah and Exceptions
Where neither kasrah nor an unvowelled yāʾ precedes the pronoun, the book generally assigns ḍammah. Its examples include لَهُ، رَسُولُهُ، مِنْهُ، أَخَاهُ، رَأَيْتُمُوهُ.
In مِنْهُ, the preceding nūn is sākin, not yāʾ. In رَسُولُهُ, the preceding lām has ḍammah. Both therefore have هُ.