The book says ṣilah does not normally occur when the letter before or after hāʾ is sākin. In مِنْهُ, the preceding نْ is sākin; the hāʾ has ḍammah but is not prolonged by ordinary ṣilah.
The short vowel remains. What is absent is the extra long-vowel sound.
Opening interactive controls...
No regular ṣilah after sukūn
Rules of Hāʾ al-Ḍamīr: Vowels, Ṣilah and Exceptions
The book says ṣilah does not normally occur when the letter before or after hāʾ is sākin. In مِنْهُ, the preceding نْ is sākin; the hāʾ has ḍammah but is not prolonged by ordinary ṣilah.
The short vowel remains. What is absent is the extra long-vowel sound.