The FI(A) does not include a CRI(A) it just happens to have a number of equivalent privileges.
I hold as independent ratings the FI, CRI SE/ME and IRI. My FI has the statement FCL.905.FI applies as in (a)/(b)/(d)/(e)/(f)/(g)/(g)(IR(R)/(h).
My CRI has For SEP(Land)/SEP(Sea)/MEP/SMG92/Cessna SET/Do28
My IRI just says FCL.905 IRI(A) applied.
Now if you go look them up you will see that there cross equivalency between the ratings but they are not embedded.