The Reason OBE exists is because the programmers offer these Functions that make no Accounting sense, such as, "Oh, you just added a bank account; let's put in the balance, too!" The same is true for, "Oh, you just added a customer name, and if they already owe you, let's put that in, too." Now you have generic AR.
You are never asked, "What do they own you for, is some of that income and some sales taxes, did you report it in the prior year or will it need to be income in the current year, where did the money in the bank come from, if you have inventory items on hand, add that quantity now and we can pretend you just found them in the gutter or pulled it out of thin air. And since we don't know what it really is, let's dump it into Opening Balance Equity!"
You see folks recommending to use OBE, because they Don't Know better. There is no reason to use OBE, when you know it Is Equity and you know the Real Equity or the offset might not even be equity at all! Let's just dump every offset into OBE and we will handle it Again, later, when we realize OBE is a generic dumping ground that needs to be 0 and never used again, once the file is set up, if it was used at all.
This isn't the same thing: "by the fact that the A/R and A/P balances would have already been reported in the prior period"
You stated they are Still Open. That is part of a Transition, then.
"and only waiting to receive cash and disburse cash for the expense."
Yes, exactly. You have Open AR and Open AP. These details Matter. That isn't OBE. It's real Details.
"the grants receivables would have already been reported as income/revenue in 2018 and the accounts payable would also have been reported in 2018."
That's why you Put in the Real Details and date it to match that Real Date you have for the invoice in 2018 and the bill in 2018. By doing this, they "roll" into Equity for you, as of the first date of 2019.
"Now, to record the Opening Balances in my new QuickBooks File at 1 January 2019 or 31 December 2018, if I were to use the forms (create invoice and enter bill) to record A/R and A/P Opening balances, I was wondering if I would be double-counting revenue and expense? For example, at January 1, 2019, my Opening would be recorded as follows:"
You need to Avoid using Debit-Credit in QB, because there is no JE for AR or AP. The Debits and Credits are behind the scenes. Enter the invoice; you just stated you want to list the Service Item that is linked to Grant Revenue; date it Historically, to match your real historic date. Once you Save this transaction, open it and use Ctl Y. Here you see the Credit to Grant Revenue and the Debit to AR. It did it For You. Use the Functions. Invoice, by definition, Debits AR, because that is its Function.
Likewise, use Vendors menu > Enter the Bill that still is unpaid for its original Historic date and list the Web Hosting here and the Customer (and billable or not). A Bill, when looked at using Journal View or Ctl Y, will Debit Expense and Credit AP for you. The bill = the AP part, because that is the Function's reason to exist.
"And these are the same entries I would have used in 2018 to record A/R and A/P."
In QB, use the Input Forms. Enter Bill for AP. Create Invoice for AR.
"I believe, you are saying that I should booked the outstanding A/R and A/P in the new QB file, indicating the relevant customer: jobs and classes just like I would if I am entering new A/R and A/P."
Exactly. When the details matter, you enter the Actual Details. You don't have "generic trial balance" when you have AP and AR. You have Name-related Activity to enter properly.
