As a general rule Norman's reply is correct but it could depend on the contract between the broker and lender.
1002.9
(g) Applications submitted through a third party. When an application is made on behalf of an applicant to more than one creditor and the applicant expressly accepts or uses credit offered by one of the creditors, notification of action taken by any of the other creditors is not required. If no credit is offered or if the applicant does not expressly accept or use the credit offered, each creditor taking adverse action must comply with this section, directly or through a third party. A notice given by a third party shall disclose the identity of each creditor on whose behalf the notice is given.
Official Interpretation
9(g) Applications submitted through a third party.
1. Third parties. The notification of adverse action may be given by one of the creditors to whom an application was submitted, or by a noncreditor third party. If one notification is provided on behalf of multiple creditors, the notice must contain the name and address of each creditor. The notice must either disclose the applicant's right to a statement of specific reasons within 30 days, or give the primary reasons each creditor relied upon in taking the adverse action—clearly indicating which reasons relate to which creditor.
2. Third party notice—enforcement agency. If a single adverse action notice is being provided to an applicant on behalf of several creditors and they are under the jurisdiction of different Federal enforcement agencies, the notice need not name each agency; disclosure of any one of them will suffice.
3. Third-party notice—liability. When a notice is to be provided through a third party, a creditor is not liable for an act or omission of the third party that constitutes a violation of the regulation if the creditor accurately and in a timely manner provided the third party with the information necessary for the notification and maintains reasonable procedures adapted to prevent such violations.
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The opinions expressed are mine and they are not to be taken as legal advice.