Traditional "built-up" felt roofs (installed properly) have been known to last for 25 years. They are torched-on these days. That is to say, pre-tarred felt and a big blowlamp.
I had my garage/workshop finished with just that recently.
But............ the chap I use is kosher. (I worked with his father before him as well.)
I say this because the flat-roofing business is plagued with idiots.
Also, fibreglass is fine IF done properly.
For my balcony, I went for EPDM, and installed it myself. Very easy. All instructions included in the kits.
So, compare prices and choose from any of these, but do choose a reputable installer........... probably NOT the cheapest one.
Your sister's main problem is that she has left it too long. It should have been renewed as soon as damp patches started to show.
By now, the leaks mat well have rotted the timber deck under the felt. That would have to be replaced, if so.
A good installer would be capable of replacing the deck as well.
In short, the installer is way more important than the method used.
Good luck :o)))