I think it is because the conductor sphere is initially neutral. The external mass m2 will induce it and make the sphere charged. As the charge on the sphere is evenly distributed on its surface, it will have attractive forces acting on m1. However, as the sphere's force on m1 is for every direction and of the same magnitude, then the net force acting on m1 will be zero. Thus shielding effect occur, m1 will not be attracted to m2. Is it like that?
In your question you refer to two masses, m1 and m2. If m1 is a hollow conductor located in an external electric field and m2 is a test charge inside m1, then m2 will not detect an electric field, neglecting any induction due to the test charge which has so little charge as to not disturb the system being tested.
I am not quite comfortable that I have understood what you were trying to say in your question. If you need a better explanation, please ask again.
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