Resolve Target Entity with multiple entity managers

As mentioned in the comment the entity managers don't talk to each other so you have to work around it. One way is to use a doctrine listener and insert a callback that can be invoked by the getPerson method.

AppBundle\Doctrine\InsertPersonListener

use Doctrine\Common\Persistence\Event\LifecycleEventArgs;
use My\FinancialBundle\Entity\Person;
use My\VendorBundle\Entity\User;
use Symfony\Bridge\Doctrine\RegistryInterface;

class InsertPersonListsner
{
    /**
     * @var RegistryInterface
     */
    private $registry;

    /**
     * Insert the registry into the listener rather than the entity manager
     * to avoid a cyclical dependency issue
     *
     * @param RegistryInterface $registry
     */
    public function __construct(RegistryInterface $registry)
    {
        $this->registry = $registry;
    }

    /**
     * On postLoad insert person callback
     *
     * @var LifecycleEventArgs $args
     */
    public function postLoad(LifecycleEventArgs $args)
    {
        $user = $args->getObject();

        // If not a user entity ignore
        if (!$user instanceof User) {
            return;
        }

        $reflectionClass = new \ReflectionClass(User::class);

        $property = $reflectionClass->getProperty('personId');
        $property->setAccessible(true);

        // if personId is not set ignore
        if (null === $personId = $property->getValue($user)) {
            return;
        }

        // get the repository for your person class
        // - changed to your version from the comments
        $repository = $this->registry
            ->getManagerForClass(Person::class)
            ->getRepository('MyVendorBundle:Person');

        // set the value as a callback rather than the entity
        // so it's not called unless necessary
        $property = $reflectionClass->getProperty('personCallback');
        $property->setAccessible(true);
        $property->setValue($user, function() use ($repository, $personId) {
            return $repository->find($personId);
        });
    }
}

My\VendorBundle\Entity\User

use My\FinancialBundle\Entity\Person;

class User
{
    //..

    /**
     * @var Person
     */
    private $person;

    /**
     * @var integer
     */
    private personId;

    /**
     * @var callable
     */
    private $personCallback;

    /**
     * Set person
     *
     * @param Person|null $person
     * @return $this
     */
    public function setPerson(Person $person = null)
    {
        $this->person = $person;

        // if the person is null reset the personId and
        // callback so that it's not called again
        if (null === $person) {
            $this->personId = null;
            $this->personCallback = null;
        } else {
            // set the personId to be stored on the db for the next postLoad event
            $this->personId = $person->getId();
        }

        return null;
    }

    /**
     * Get person
     *
     * @return Person|null
     */
    public function getPerson()
    {
        // if the person has not been set and the callback is callable,
        // call the function and set the result (of $repository->find($personId))
        // to the person property and then return it. The callback is
        // reset to stop unnecessary repository calls in case of a null response 
        if (null === $this->person && is_callable($this->personCallback)) {
            $this->person = call_user_func($this->personCallback);
            $this->personCallback = null;
        }

        return $this->person;
    }
}

AppBundle\Resources\services.yml

app.listener.insert_person:
    class: AppBundle\Doctrine\InsertPersonListener
    arguments:
        - '@doctrine'
    tags:
        - { name: doctrine.event_listener, event: postLoad }

UPDATE

After looking for an example of this in real life I found this. From this I saw that you could change the

$reflectionClass = new \ReflectionClass(User::class)

to

$reflectionClass = $args->getObjectManager()
    ->getClassMetadata(User::class)
    ->reflClass

which, I assume, would mean one less new \ReflectionClass(...) call per load.