If you are not concerned with having an audit trail, then you can simply change the name of the account/qualifier so it is matched to the new brokerage account. By changing the name of the account/qualifier your investment reports along with your balances sheet will be accurate going forward, but your reports from prior months will display the new account/qualifier name.

The alternative solution and preferred method is to record the transfer of the security in a brokerage journal.

This will require three journal entries:

1) Sell the security being transferred at cost. Enter this transaction in the brokerage account making the transfer.

Journal/Account: Brokerage Account 1
Debit/Credit: Debit
Date: Transaction Date
Payee: Transfer Security
Account: Stock being moved
Amount: Cost of Security

In the Multiple Distribution window that appears, there should be no amount in the Capital Gains or Loss Account. The only accounts affected are the Security Account, Unrealized Gains or Loss Account, and the Brokerage Account.

2) Transfer the funds to the new brokerage account. Enter this transaction in the brokerage account making the transfer. Make sure you have your Transfer Clearing Account setup.

Journal/Account: Brokerage Account 1
Debit/Credit: Credit
Date: Transaction Date
Payee: Transfer Funds
Account: Brokerage Account 2
Amount: Cost of Security

3) Buy the security at cost in the new brokerage account.

Journal/Account: Brokerage Account 2
Debit/Credit: Credit
Date: Transaction Date
Payee: Transfer Security
Account: new name for stock (must be different from prior account name)
Amount: Cost of Security

Multiple Distribution Window:
Date: Original Purchase Date
Quantity: Original Amount
Tax Basis: Same as transfer amount

After entering the three transactions, go to the Chart of Accounts and change the tax code for the security transferred to No Tax Effect. Not changing the tax code will cause the security transferred to appear on the Schedule D.

Now you have properly accounted for the transfer of a security from one brokerage account to another.