The link you shared earlier doesn't seem to work anymore (please see below). I am also having the same problem as the original poster. My sprocket won't connect to my new iPhone XR, which I just upgraded to.
https://support.hp.com/us-en/product/hp-sprocket-photo-printer/12635221/document/c05300073 (HP Sprocket - Cannot Connect, Print, or Update Firmware (Apple iOS)
I have deleted the app, reinstalled, turned off my phone and the sprocket and restarted them. However my phone is still not able to discover the Sprocket.