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Yes.  Two options for 1099s sent to the estate:

• You have an estate ID. You can do an estate return, report the forms, and issue the k-1 to the beneficiaries to put on their returns. Use the Business Software for Estates
• You can file the necessary /same 1099 forms from the estate to the nominees. Topic No. 403 Interest Received states:

There are times when you may receive a Form 1099 for interest in your name that actually belongs to someone else. In this case, the IRS considers you a nominee recipient. If you received a Form 1099-INT or Form 1099-OID that includes an amount you received as a nominee for the real owner:

• See "Nominees" in the Instructions for Schedule B (Form 1040) for how to report the interest on your income tax return.
• You must then prepare a Form 1099-INT or Form 1099-OID for the interest (or OID) that's not yours unless that interest (or OID) belongs to your spouse. Send Copy A of the 1099-INT or Form 1099-OID and a completed Form 1096, Annual Summary and Transmittal of U.S. Information Returns to the Internal Revenue Service and give Copy B to the actual owner. For more information on these requirements, refer to the Instructions for Form 1099-INT and 1099-OID 

Once your have filed either the 1041 estate or the 1099 forms, there will not be anything else needed to send to the IRS.