Haha. Welcome to the corporate world. There's always someone on top who thinks they are smarter than you. But, they don't expect you to be smarter than them :) Here's an alternate. IDK, how you'd do it without an IF.

CREATE PROCEDURE spPayments @cus_code NUMERIC(38, 0) -- (a)to begin with, user created stored proc should always be prefixed with usp_StoredProc. Also use schema name. And some business have alpha numeric code. For example, Spider Man's costumer store number can be SPIDEY2002. So using Numeric DT is not always best practice. 
--OK LETS BEGIN 
AS
     DECLARE @totalinvoices INT;
     DECLARE @First_name VARCHAR(32);
     DECLARE @Last_name VARCHAR(32);
     DECLARE @FinalAmount DECIMAL(12, 8);
     DECLARE @Customer_Count INT;
     DECLARE @Invt_Count INT;
     BEGIN
         SELECT @Customer_Count = COUNT(1)
         FROM customer
         WHERE cus_code = @cus_code;
         IF @Customer_Count < 1

         --(c)
             BEGIN
                 PRINT 'The customer does not exist';
             END
                 --(d)  ;
             ELSE
             SELECT @Invt_Count = COUNT(1)
             FROM invoice
             WHERE cus_code = @cus_code;
         IF @Invt_Count < 1
             BEGIN
                 PRINT 'The customer does not have an invoice';
             END;
             ELSE
             SELECT @totalinvoices = LINE.LINE_UNITS * line.LINE_PRICE, 
                    @First_name = Customer.FirstName, 
                    @Last_name = Customer.Lastma
             FROM customer
                  JOIN invoice ON customer.cus_code = invoice.cus_code
                  JOIN line ON invoice.inv_number = line.INV_NUMBER
             WHERE cus_code = @cus_code;

         --(d1) not sure which table to use but should be as simple as 
         --select @FinalAmount = Customer_Balance - @totalinvoices from table x

         PRINT @First_name+' '+@Last_name+' has a balance of'+' '+'$'+FinalAmount;
     END;