powershell is like any other windows command line tool 
a simple .ps1 script with the following will do the copy
copy source destination
or
copy-item source destination
or
robocopy source...

Adding a bit to this - first the annoying bit. this has been posted on at least 4 sites. 
This can lead some of those that know a possible answer...

This is a lot more complex than what you think.
Look at one approach https://www.youtube.com/watch?v=JJryD2dXVVw- does have issues that I am not sure have been solved in the meantime.

I would not even try to figure out what is causing the issue - you are still on the first version of 2014 - upgrade that to the latest SP ...

convert to date
select max converted date

and fix your tables - dates should never  be stored as anything other than dates .

one other option is for the job that does the first snapshot to start the second job on the other server as the last step on the job.

My assumption, by reading the sql posted, is that the hash is done as part of the load of tbl_Staging_Current_SubjectXYZ.

so one of the approaches I was suggesting is

Plan not attached. -- saw it now.

The main performance improvement on this type of process is using the hash compare as you do.

Following are possibilities -...

then as per the error the file can't be opened - pretty clear - and just proves that you didn't really search for anything - just expect that we do...

not enough really - just on the forums here you get 99 hits
and please post the full error message, not just a screen print that does not show the...

have you even bothered googling for it? first hit I get has the reason for the issue and the solution.

also take in consideration that having compression turned on (page or row, or even columnstore) will change the space requirements. many times significantly, specially with columnstore.