bpo-45125: Improves pickling docs and tests for shared_memory (GH-28294)

Doc/library/multiprocessing.shared_memory.rst

@@ -342,3 +342,30 @@ behind it:
    >>> c.shm.close()
    >>> c.shm.unlink()
 
+The following examples demonstrates that ``ShareableList``
+(and underlying ``SharedMemory``) objects
+can be pickled and unpickled if needed.
+Note, that it will still be the same shared object.
+This happens, because the deserialized object has
+the same unique name and is just attached to an existing
+object with the same name (if the object is still alive):
+
+   >>> import pickle
+   >>> from multiprocessing import shared_memory
+   >>> sl = shared_memory.ShareableList(range(10))
+   >>> list(sl)
+   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+
+   >>> deserialized_sl = pickle.loads(pickle.dumps(sl))
+   >>> list(deserialized_sl)
+   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
+
+   >>> sl[0] = -1
+   >>> deserialized_sl[1] = -2
+   >>> list(sl)
+   [-1, -2, 2, 3, 4, 5, 6, 7, 8, 9]
+   >>> list(deserialized_sl)
+   [-1, -2, 2, 3, 4, 5, 6, 7, 8, 9]
+
+   >>> sl.shm.close()
+   >>> sl.shm.unlink()