Is HP Toolbox available for the Office Jet 2622 printer?
I didn't find enough information to say that HP Toolbox is compatible with your device, however, I've checked a manual and I've seen instructions related to HP Toolbox. For example, there were details on how to access the HP Toolbox through the Maintain your Printer. However, for that to be possible you will have to download the FULL INSTALLATION PACKAGE available on the HP website.
Use the following link to access the full driver installation package: http://support.hp.com/us-en/product/HP-Officejet-2620-All-in-One-Printer-series/5357283/model/5385219/drivers
Note: Make sure to download the manuals as well.