Add with function():

AStrings.AddObject(Name, TObject(string(Path))) ;

Test in OnChange:

ShowMessage(string(cbList.Items.Objects[cbList.ItemIndex]));

First ShowMessage() is showing path and then raises EInvalidPointer. How to fix it?

The most direct way: Use a global variable for your string. But that can still end up in all sorts of messes because of the compiler magic strings come with. Especially fun stuff like copy-on-write related things.
(Edit, to be clear: Do NOT do this! It may work in some special and simple cases, but is dirty like whatnot.)

A more sensible way: Define a TStringList in a suitable scope, and put the index of your desired string from that list into your Object-Property. To read it, just use that index on your StringList. You'll save yourself a lot of potential trouble that way

Or simply use a real TObject containing a string property

Do not cast string, dyn. array oder interfaces.

This bypasses the reference count.

Thanks, I created class for this purpose