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Since Method does not implement Serializable, it cannot be serialized using the standard Java Serialization API.
A workaround would be to manually serialize just the name of the class and method and its parameter types. You can then recreate the Method instance during deserialization.
If you just wonder, is it possible, than no: it doesn't implement Serializable. Also, Method is a final class, so you can't subclass it in order to add some functionality.