Who said you're heart can't be in two places.
She was spared the final stages of the disease by the transplant, and it's preserved condition, is a reminder to her of the condition her heart was in, and how it was losing it's ability to do it's job. It is also a reminder of what her mother suffered, as she can see a clear example of what the disease had done to her, too early to find the same solution.

Indeed it's quite a story, but also a tad creepy. Looking at bits and pieces of one's innards floating in a jar is a bit 'jarring'.

Obviously it is not a healthy heart - I remembered in my anatomy class we held donors' heat in our hands. They all looked red and healthy...maybe they took away fat tissue.