Battling for days with FindFirst (Help)

I would be delighted if someone could help me resolve this problem.
I am trying to add a record to a table but;

1. Check that the input is not Null
2. If the input is not Null, check if the name does not exist already
3. Add a record if the name does not exist.
4. If the name exist already, store the person's address in a variable to display on a form

The code below works fine except for point 4. It always display the address of the first record in the table.

Please help!! Many Thanks


Dim db As DAO.Database
Dim rsMembers As DAO.Recordset
Dim NewName As String
Dim NewAddress As String

Set db = CurrentDb()
Set rsMembers = db.OpenRecordset("tblShareMembers", dbOpenDynaset)

If TransfereeName <> "" Then
NewName = TransfereeName

Dim rst As DAO.Recordset
Dim MemberName As String

Set rst = db.OpenRecordset("tblShareMembers", dbOpenDynaset)
MemberName = "Name = '" & TransfereeName & "'"
rst.FindFirst MemberName

If rst.NoMatch Then
' Call the function that adds the record.
AddMembers rsMembers, NewName, NewAddress
MsgBox "You must enter the Transferee's Name and address.", , "Fairview"
rsMembers.Close
Else
TransfereeAddress = Address
End If

Set rst = Nothing
Else
MsgBox "You must enter the Transferee's Name and address.", , "Fairview"
End If