It is exceptionally rare for history UDFs to be added automatically.  (Only SO_SalesOrderHistory... tables do this as far as I know).

Add UDF's to AR_Invoice... tables only if you use AR Invoice Entry (which I generally discourage in systems with SO). 

You can set up the history UDF data sources from multiple directions (...see tab 3 when setting up the UDF).  Watch for middle steps (like AR_TransactionPosting for invoice header UDF's).  You need to set up each link, for each data source.

Thanks!

This was enough to get me going. 

For those who need to do the same, I will try and explain what I did.

I wanted to get AR_InvoiceDetail user defined fields entered in AR Invoice Entry to make it through to AR_InvoiceHistoryDetail when I posted the batch.

I had to add the fields to AR_InvoiceDetail first.

Then I had to add the fields to "AR_Sales Journal Work".  When doing so, it required that I enter a source for the data.  For each field, I picked the AR_InvoiceDetail table and the corresponding UDF column.  How did I know to edit "AR Sales Journal Work"?  It is kind of a guess based on what I saw as "Data Source" options for the AR_InvoiceHistoryDetail columns.  There I saw "AR_SalesJournal_upd".  There is probably a link between this and "AR Sales Journal Work" in the Sage business object documentation.  

Finally, I added the fields to AR_InvoiceHistoryDetail.  In this field setup, on the "Data Sources" tab, I selected the checkbox next to AR_SalesJournal_upd.   This enables the Source and column fields.  In those select "AR_InvoiceDetail" and the corresponding UDF column.  

By the way.  We are using AR Invoice Entry only for non-sales order related transactions.  Our sales order invoices go through the SO_Invoice modules and don't need these user defined fields.

Thanks!