Easiest would be to include Firstname and Lastname as separate columns in
the combo box (you don't have to display them):

SELECT tbl_Employees_records.PERSON_ID, [LASTNAME] & ", " & [FIRSTNAME] AS
FULLNAME, [LASTNAME], [FIRSTNAME]
FROM tbl_Employees_records
ORDER BY [LASTNAME] & ", " & [FIRSTNAME];

You'd then refer to columns 2 and 3 to get them.

With your current setup, you could use the following in the AfterUpdate
event of the combo box:

Private Sub cmb_names_AfterUpdate()

Dim strFirstName As String
Dim strFullName As String
Dim strLastName As String

 strFullName = Me!cmb_names.Column(1)
 strFirstName = Trim$(Mid$(strFullName, InStr(strFullName, ",") + 1))
 strLastName = Trim$(Left$(strFullName, InStr(strFullName, ",") - 1))

 Me!txtFirstName = strFirstName
 Me!txtLastName = strLastName

End Sub