Loading mat files does not support enumerations with function handles?

I basically have an enumeration class with one property being a handle. After saving an instance (TestEnum.a) to a mat file and loading it again I am facing the following warning:

Warning: The value of enumeration member 'a' differs from when the enumeration was saved. 'a' will be loaded with the new value.

Why is that the case? I have noticed that this does not happen in case the property is anything else?

classdef TestEnum
 
    properties
        hdl 
    end
    
    enumeration
        a (@(x) x)
    end
    
    methods
        function obj = TestEnum(hdl)
            obj.hdl = hdl;
        end
    end
end

Answer 1

[Steven Lord]

The question of whether two function handles are the same is a bit complicated.

[Max Mund]

Okay I understand the issue but what options do I have to work around it?

Customizing the save and load process was my initial idea. Unfortunately I have noticed that for enumerations the loadobj(s) function is never called.