Charge the freight bill to the inventory GL account #.  Manually adjust the value of the part in question through IN-K

Karen is right, the GL Posting will occur only once when you enter tthe freight invoice.  Editing the Average Cost in IN-K will not make a GL posting.  You will need to run UT-K-G to get book value in line.
 
For future, you may want to use the Freight Percent in Inventory to automatically burden inventory for freight.

There is a default account on the AD-A, Mfg Defaults screen for the "Absorbed Freight In".  It should be an expense account next to your Freight In Expense account and will carry a credit balance offsetting the debit in Freight In.  Posting will process as follows:
 
Establish (as an example) a 10% freight percentage in IN-B for an item.
 
PO-C for 100 each @ $1.
Program will add 10% to inventory value.  
Unit Cost in IN-A is $1.10
GL Posting will:
Debit Inventory $110
Credit PO/RNI $100  
Credit Absorbed Freight Account $10
 
Process Vendor Invice for $100, it contains no freight.
Debit PO/RNI $100
Credit AP $100
 
Receive third party freight bill for $12
Debit Freight In $12
Credit AP $12
 
Comparing the Freight In of $12 and the offsetting Absorbed Freight In of $10 indicates that the 10% value is not accurate.  If this fluctuation is large, consider adjusting the percentage in IN-B for future receipts.