Unable to view Web Map Service (WMS) services (Version 1.1.1) in Map Viewer without the GetCapabilities file for version 1.3.0.

Workaround

When adding a layer from the WMS Service to ArcGIS Pro (tested both in 3.3 and 3.4) and publishing the map as a Web Map in ArcGIS Online the layer becomes available also in Map Viewer.

The proposed workaround was to add the WMS layer to ArcGIS Pro and share it to ArcGIS Online:

1. Open a project or map in ArcGIS Pro.
2. Integrate the WMS Server via "Insert > Connections > Server > New WMS Server".
3. In the Catalog View, add the desired layers to the map.
4. Share the web map via Share > Web Map.
5. Now the web map can be opened in ArcGIS Online or Enterprise with the map viewer and the layer remains.

In addition, it is also possible to enrich an already created map from ArcGIS Online/Enterprise with a layer from the WMS:

1. Open the desired layer in ArcGIS Pro. To do this, click on "Portal" in the Catalog Pane and add the desired layer there.
2. Integrate the WMS Server via "Insert > Connections > Server > New WMS Server".
3. In the Catalog View, add the desired layers to the map.
4. Now save the web map via "Share > Save Web Map", this will not create a new map, but update the existing one.

Steps to Reproduce