I always point out that you should verify there is no ground actually present before going this route. There was a period in the post WWII years where they were using an NM cable with a ground but still using non grounded receptacles (NEMA 1-15). In that case the box will be grounded but no provisions for a grounded plug cap. In that case you could use the existing ground for a NEMA 5-15 grounded receptacle. The only question is whether you should trust the "self grounding" type or pigtail a ground in from the box, I prefer the latter.
The other issue is the ground in that old Romex is a reduced size but a 16ga wire should still be sufficient to clear a fault on a 15a breaker.
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