Having a digital copy is a good idea but you should also carry some form of physical document (paper /laminated /plastic member's-card) listing all the necessary insurance details. In case you get in a bad accident the medics will go through your pockets looking for it and it will decide whether you end up in the best, most expensive hospital, or the public, least desirable one. If the information is on your phone it will be inaccessible when it mostly matters. Regrettably this happened to a friend so this is not just a hypothetical scenario. On top of my insurance member's-card I also carry my agent's business card so the hospital has an alternative contact person who can brief them on the status of my insurance plan. The difference in level of care, ER equipment, and doctors' expertise between public and private hospitals in Thailand is shocking.