We usually do not respond unless their are pictures
Having said that ; after testing what your orginal mortar is
begin stabilization in sections; so you do not weaken the whole wall with
your cutting.
 Now if your back up orginal mortar is just sand ;
 test by flushing the wall with water and see where it all comes out...
Then it may be a candidate for Lime grout injection
If it is just soft yet crumbly mortar it may be fine to repoint with a
hydraulic lime mortar to match what I am guessing is the original...
...but rake  back more than 1" to fell comfortable......Lastly American
Heritage lime works is giving a hands on workshop in the Chicago area Aug 15?
 this invaluable workshop ( and ones like it ) is necessary for all craftsmen
and architects of 19 cent buildings ......maybe someone on the list has more
details ..Best Michael

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