What's the right mortar/mix for repairing solid stone wall

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Builder needs to repair this hole which he still has the stones from (pic below). He wants to use a 'standard' mortar mix and is concerned mainly with it being structurally sound.

 

It's worth noting we'll be taking some stone out below and adjacent to this to create a doorway, and that there'll be a block wall from the new extension butting up against this corner.

 

He knows I would prefer lime where the old walls are concerned but that's more relating to pointing and plaster than the repair work. Any thoughts?

 

 

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The other photo