I'm not sure you should do this as it might give you incorrect results if there are several people with same name and DOB (chances are low, but it could happen).

If you proceed with this, you could use this sample code to guide you.

DECLARE @Test TABLE(

ID int,

lastName varchar(20),

firstName varchar(20),

DOB date,

SSNvarchar(20))

INSERT @Test

VALUES

(1, 'Doe', 'John', '19670101', '111-22-3333'),

(2, 'Doe', 'John', '19670101', NULL),

(3, 'Doe', 'John', '19670101', '111-22-3333')

UPDATE t1 SET

SSN = t2.SSN

FROM @Test t1

JOIN @Test t2 ON t1.lastName = t2.lastName

AND t1.firstName = t2.firstName

AND t1.DOB = t2.DOB

AND t2.SSN IS NOT NULL

WHERE t1.SSN IS NULL

SELECT * FROM @Test