Try to look at the sharing permissions of the webmap, as well as the data (feature service) that is in the webmap. The publisher (user) needs to have access to both. Since you have it working as administrator, it sounds like it is an operational app. Do make sure the webmap has an editable feature service in there or the collector app won't recognize it.
best wishes in the recovery
So the best way to manage this is to create a 'Collector' group within an Organization and invite your field data collectors to join it. All data collection WebMaps would be shared to this group.
Sharing it with the organization doesn't make it appear in the Collector for everyone in that organization since Collector only shows content that is in "My Content" or "My Groups". The best way to share a map in Collector is to create a group in your organization, share the map with that group, and have your users who need the map be members of that group. Then they will see the map in Collector.
Also, please use the Collector forum for additional questions on this app: this forum is for the Operations Dashboard for ArcGIS application.