Apologies if this topic & solution is already buried somewhere in this forum. Note, this is about text/sms messages, not those PUSH notifications to the Ring App that are only received if/when you have a data service (or WiFi) active. The importance of receiving text/sms can be critical, and is why this feature is available in other home alarm products (not Ring).
The easiest solution I came up with to received text/sms (or multi-media - mms) messages on my cell phone is to have the Ring Alarm user account email located on a service that allows mail filters & forwarding. Gmail is one example.
Simply create a forwarding address from the email account of your Ring user to your cell phone, and then create a mail filter using whatever parameters you see fit.
For my filter example on Gmail I created one to specifically forward just a “Ring is Alarming” email to my cell phone as an alert text message. To do this I used a filter containing - from: “rs.ring.com” and subject: “Ring is Alarming”, targeted to my AT&T cell: “<10 digit number>@mms.att.net”. Tip: sending notifications to MMS results in a better display of most Ring messages and any associated hyper links.
It is obviously possible to add more filtering or additional separate filters if you wish, and also do this email fowarding from any or all of your Ring user account emails (ie: the spouse’s user account).
For a good list of text or mms providers, see this link: