from what I gathered out of this (been a few months so I may have misremembered parts), the girl aged no faster or slower than he did. All that happened was that the ship shifted position in relation to earth, causing the transmission to have to cross a farther distance and hence take a longer amount of time each way.
So, as long as the ship stays X lightyears from earth, it will take X years for a message to traverse the distance, and another X years for the response to reach the ship. The perspectives shown in the film are seperate in both space and time, connected only by the fact that a message sent in one time is just arriving in the other. It has been days/weeks/months at most for her, and definitely years for him, but in no part to time manipulation or such. Events show are not occuring concurrently.
Now, one problem exists that it is quite possible that the ship could jump over a signal, going from an area that the signal has yet to pass through to an area the signal has already passed through, thus causing the ship to completely miss the response, wheras Earth is a relatively fixed point and thus will receive most (if not all) tranmissions aimed at it.
And, with response to the return voyage, based on his actions the ship has yet to return, so she has either aged so many years as well or died sometime during the return, that is left to the imagination, all that is needed to know is that the ship has yet to return by the time the text messages arrive at Earth.
However, when the ship arrives, they will both have aged the same amount since the last time they encountered each other, with any differences being extremely minor, assuming (of course) that her ship uses faster than light travel methods.
If not, then the closer to lightspeed you reach, the slower you experience time, and thus she would experience less time than he did, but for purposes of the story this is speculating about what happens after the end credits.
Hopefully that makes some sense.
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