Find the local unitary that takes the bell state to a state phi that has an extractable bell state

I have a state $|prangle$ that has an extractable Bell state and I want to write it as a Bell state, $|brangle$, with a local unitary acting on one side. Basically I am trying to find a local unitary $U$ that satisfies:

$$
|prangle = (U otimes 1)|brangle
$$

$|brangle$ is a Bell state
$|prangle$ is a known state with an extractable Bell state

Does anyone know how to do this?

My initial guess was $U otimes 1 = |p rangle langle b|$ but this isn’t a unitary operator.

The known state $|prangle$ is in state vector form. I am using Python an NumPy for reference.