Seems odd the surveyor would use XYZ or ECEF?
We’ll… u may want to contact MicroSurvey for help since XYZ.
I haven’t really thought it through and I don’t have Field Genius, but maybe you could ‘fake it’ by using ENU (East,North,Up) output from ReachView to FieldGenius? That gives the base a coordinate of 0,0,0. I’m not sure how you’d localize to one of his points. Maybe you could shift the 0,0,0 origin in your cad drawing to a point that you can put your base on.
disclaimer: This is most certainly not the right way to go about it, which is why I used the term ‘fake it’.
(keyphrase for researching ENU: “tangent plane”)
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Hmm. If you traveled 4.5km south and 3km west, what would you see? Some kind of marker? The surveyor’s office? A local NTRIP station? Or does it just happen that you are that close to the origin point of a local grid?
edit: You could put your base on one of the listed coordinates. Then use the rover’s ENU output through an app (FG?) to navigate to the negative values of the coordinate that your base is on. When you arrive there, you can find the surveyor’s origin point to satisfy your curiosity (and mine 
). Depending on distance and line-of-sight it might be a bit of a challenge to set up for RTK - maybe not worth killing the cat on this one.
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FieldGenius ANDROID has ECEF basis? Maybe there’s your solution when released? But expect bugs etc early in.
https://rplstoday.com/community/software-cad-mapping/android-field-software/
Also note the XYZ system in the video:
https://www.microsurvey.com/fga/
(Looks like UTM to me?) 
Cedar CT8 $999. What mount is he using?
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Trying to catch up with this thread so excuse me if this has already been asked. Where are you? I am pretty sure that those coordinates are not from a state plane coordinate system. They are from a fictitious grid, but fieldgenius should not have a problem localizing them.
Traditionally when you localize the base station coordinate does not matter. Set up wherever you set up and then you check into the other control points. The data collector should be working off of wgs84. The program assigns a GPS coordinate to that XYZ coordinate and then to all the other control points. It is a pure distance to base scenario.
This may be a limitation of the reach receivers. One word of advice to create the fictitious XYZ coordinate for the base as close to the general position on the site so that when you zoom extents it doesn’t go out so far that you can’t see your site anymore.
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