Is there a way to send to the client a "thanks" when receiving the order or after invoicing?

It would be my pleasure to help you thank your clients for their business, @rshlesinger.

I'll guide you through doing so below:

Sending a Received Payment Message

1. From QuickBooks Online, click the Plus (+) icon and select Receive Payment.
2. Select the client, enter a deposit account, and check off the Invoices/Orders you're receiving.
3. Click Save and send at the bottom. The Send Email preview window will appear.
4. Enter the client's Email, a Subject, and a Message. Click Send and close.

We also have an awesome guide on customizing customer messages that I'm sure you'll find helpful. I'm including a quick video demonstration of this below:

With these instructions, you can let your clients know just how much you appreciate their business. Please touch base with me here should you need any additional assistance, I want to ensure your success. Thanks for coming to the Community, cheers to a productive rest of the week.