I'm 62, getting ready for retirement, and in a similar situation. I worked for a dozen years at Microsoft, purchasing ESPP, getting stock grants, etc. My stay there nearly exactly coincided with Steve Ballmer's turn at CEO. During that time (except a large drop right after I started and a dip/recovery in 2008-2009), the stock remained completely flat. Though MSFT made up a sizeable, but not overwhelming, chunk of my wealth, it paid a good dividend and I was comfortable that it wasn't going to drop (like it did right after I started with the company).
Since I left that company, the stock price has quintupled and it now represents not quite 50% of my assets. It might make sense to sell off a large chunk and rebalance my portfolio, reducing my exposure to that one stock - but that comes with a large capital gains hit.
But, you know what - it pays a very good dividend, and though I'm not convinced that it's current run of growth will continue, I don't see it dipping more that 10 or 20%. My financial advisor and I have had long talks about this (i.e., "he knows his customer"), and I think we've come up with a plan that will slowly reduce that exposure. I realize that this may be crazy, but, it's worked so far.
As to your 80-year-old mother... she's got a MM$3.5 nest egg to spend over her next 0-20 years. Talk to her about the risks and make sure that she understands what she's doing (don't forget, JPM has grown a lot in the last 10 years -- she may be very happy with what she's got). If she understands what her situation is and what the risks are and is still comfortable, let her enjoy her wealth.