about how to parse the possessive compound?

The Shaykh : No, this is declinable. It is not a compound; this is parsed as a possessive compound. Its first part is parsed on its own, and its second part is always in the genitive case due to the possessive relationship.
The student: What is the exception?

The Shaykh : What is the exception? Because here there is a barrier preventing declension, meaning a barrier to it being indeclinable, which is the possessive relationship. The possessive relationship is in its first part, and the article (al-) is in its last part.