You seem to misunderstand what lookbehind is for. What's more, you don't even need it. You wrote:

$string =~ /Periodic Reports','(?<!.*'$)/;

Just change this to

$string =~ /Periodic Reports','(.*?)'/;
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and now you'll match what's in the single quotes after "Periodic Reports" (etc.).

If you insist on using lookbehind, use it for what it's for: "Does what I match now follow something looking like this?"

$string =~ /(?<=Periodic Reports',)'(.*?)'/;
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Read it as: "match what's between single quotes, but it has to come after the string "Periodic Reports',".