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This page covers the possessive form of compound nouns and joint ownership.
Because these constructions stretch the resources of punctuation beyond comfort, in practice they are normally reworded: interventions by successive Ministers for Justice.
It makes no difference whatsoever to where the apostrophe goes.
When you connect two words, an apostrophe is a grammatical glue that holds them together.
This is similar to the practice in Pinyin mentioned above.