More variations on the theme (if I got it right - the Z is repeated though). The second one does not use captures at all.

while (<DATA>) {
  print;
  #s/^A(|\s[^Z]*)Z$/A$1IZ/;
  s/^A(?:|\s[^Z]*)\K(?=Z$)/I/;
  print;
}

__DATA__
AZ
AZZ
A SOMETHING Z
ASOMETHINGZ
A  Z
A ZZ
AAZZ
AA ZZ
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