I can't believe I found a solution to this and no one from QBO has been able to come up with it.

My Situation: I had an estimate that was approved. We do progress billing. We have had 2 invoices already billed and paid against the approved estimate. We have 1 invoice due from the client yet to be paid. I upgraded to Plus to be able to track each project separately. When I followed QBO experts' directions and changed the customer dropdown to the project name the entire invoice cleared out. 

Here is the workaround I found:

1. Create your Project.
2. Now, go to Sales and click on Invoices.
3. Go to the invoice that you want to migrate to your project and click on the "▼" Down Arrow on the right hand side (next to Edit | Print | ▼ ). Select Duplicate
4. The duplicated invoice will show up in your invoices tab with the same customer name and Amount as the original but it will have a different invoice number and will be marked as unpaid.
5. In the duplicated invoice go to customer dropdown and click on your project name.
6. You will now have 2 invoices with the same Amounts listed in your Invoices tab. 
7. You will have to go back and mark your Duplicated invoice as paid manually.
8. To make everything match exactly, you can go into your Duplicated Invoice and change the invoice number to match the original invoice number.
9. You will now see that the duplicated invoice labeled as "Customer Name": "Project Name" instead of just "Customer Name" 
10. The duplicated invoice will be what is in your project under the projects tab.
11. Once everything is as it should be, you can either Void or Delete your original invoice that you were unable to migrate to Projects.

Doing this saved me from having to recreate my invoices line by line (we break down our quotes by activity on most of our contracts, so most of our estimates and invoices have 20+ lines in them.) Hope this helps someone...

I appreciate your participation in this thread, EBGKamin.

We in the Community thank you for sharing the workaround you've discovered. Your input is essential for users to manage their estimates, invoices, and projects accordingly. Please know that your thoughts and insights are always valued.

You may also set up and use projects for the QuickBooks Time Elite plan. For more details, kindly refer to this link: Manage projects for QuickBooks Time.

Our purpose in the Community is to ensure all users can manage their company seamlessly in QuickBooks. If you have more questions about converting invoices, estimates, and projects or need assistance with your reports and data, hit the Reply button. We'll ensure you're taken care of.

This sounds promising. I will try it out next time. Although, since I originally posted 4 years ago, and Quickbooks never came up with anything, I have done all I can to avoid having this problem, which in itself is annoying.

I still can't believe they didn't fix it. I still don't see, how we can add quotes to the project without loosing anything, but they haven't figured out how to do the same with invoices.....

I was able to add my estimates without issue. 

I simply went into my estimate and selected the project name. 

Then, in the project tab under "Transactions" tab the estimate was added. 

One thing i did note, once you add your estimate in the project, NOTHING CHANGES. You won't see anything in the "Income vs Cost" bar graph. You will only see these values fill out once you actually convert the estimate to an invoice (or migrate invoices into the project)

For some reason, the dashboard does not have any indication of the estimate at a glance. you have to go to the Transaction tab to see your estimate. The entire Projects tab seems to function only on invoices billed to date. And it does not seem to take into account what your balance to finish is. 

Im also very new to QBO so maybe i'm missing something, or have a feature turned off.