1. Both accounts are “owned” by the same person, in which case the entities may be set up incorrectly. You may want to move all the accounts from one entity over to the other. Then transfers would be easy.
Or
2. The two entities are really separate – perhaps one is a trust and the other a person. In that case, the trust is making a payment to an outside party (Entity 2), and the person is receiving income from an outside party (Entity 1).

I would set up a Payee account in the Trust for “Person” and a Payor account in Entity 2 called “Trust Income.” Then show a sale in the Entity 1 brokerage account, and pay the cash to Person. Then receive the cash as income in Entity 2 and use it to purchase the same security at the same price.

This may create tax issues, as it should, unless the transfer is tax exempt.

If you have access to the Navigator Resource Center, refer to the excellent topic Gifts of Securities.