Memoizing a tree's parent pointers in Python

I have a simple binary tree that has no parent pointers.

class Node:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

class Tree:
    def __init__(self, root=None):
        self.root = root

I need to traverse the tree from bottom up and cannot modify the Node class, so I'd like to memoize the parents. I can modify the Tree class as such:

class Tree:
    def __init__(self, root=None):
        self.root = root
        self.memo = {}

    def memoize(self, node, parent_node):
        if node is None:
            return False
        self.memo[id(node)] = parent_node
        self.memoize(node.left, node)
        self.memoize(node.right, node)

    def get_parent(self, child):
        return self.memo[id(child)]

If I create a tree, memoize it, and run get_parent() I see what I expect:

a = Node(1)
tree = Tree(a)
b = Node(2)
c = Node(3)
a.left = b
a.right = c

tree.memoize(a, None)   # Tree root is instantiated with no parent
parent = tree.get_parent(b)

print(tree.memo)
>>> {4405793712: None, 4405793856: <__main__.Node instance at 0x1069b13b0>, 4405793928: <__main__.Node instance at 0x1069b13b0>}

print(parent.val)
>>> 1

This seems to work nicely. However, I am a Python beginner, and want to know: is there a more Pythonic way to do this?