Shapefile lines up differently in ArcGIS Desktop 10.5.1 and ArcGIS Pro 2.0

[AllenRisley]

I have a shapefile that I use regularly in ArcGIS Desktop (now 10.5.1) and the shapefile lines up properly with the ArcGIS Imagery basemap.  The shapefile is projection is Lambert Conformal Conic, projected coordinate system is NAD_1927_StatePlane_California_VI_FIPS_0406 .  When I add the shapefile to a map in ArcGIS Pro 2.0 with the ArcGIS Imagery basemap I get different results.  The features in the shapefile are shifted about 260 ft to the west.

I'm assuming that this is a projection problem and that I need to reproject the shapefile, but I'm confused as to why the results would be different between ArcGIS Desktop 10.5.1 and ArcGIS Pro 2.0.

Any ideas?

[MervynLotter]

This is a datum issue I suspect, not a projection one. You may find that in ArcMap a transformation has been set on your data frame, but not in ArcGIS Pro.

In Pro you need to right-click on the Map properties heading, then select Transformations and try and find a suitable transformation method between the datum of your basemap and that of your shapefile. 

I found a great tech video from Dev Summit 2017 on introducing projections and coordinate systems here (and includes a great overview of vertical coordinate systems)  Introducing Coordinate Systems and Transformations - YouTube . Perhaps this may help.