Offered flight prices are often dependent on your location, for the same flight with the same airline. Typically, if you are in a poorer country, flights are cheaper, and if you are in a richer country, they are more expensive. Check for example Google's flight search (http://matrix.itasoftware.com/), which allows you to pick the 'location' you are booking from.
In addition, the conversion to different currencies is done only once, with a margin, and then used for months, so by the time you book, it could be off a lot. For example, if the airline wants 1000 US$, the booking sites all over the world convert that with a fixed rate - they will have to pay 100 US$, but because you are in country X, they ask N of X's currency, which needs to be enough when they have to pay.
- If there is enough trust, you can type in all the data and pay with her credit card, as if she would be in the location you are in.
- She can use anonymity websites that make her appear to be in a different place (i.e., having another IP)
- You can book for her, with the slight risk that someone wants to see the credit card at check-in. I have never ever seen that (and I fly 50 times a year for decades), but people keep claiming it happens. You can send her a photo of the credit card, that might work, but if that is real, it could be an issue.
You might be able to avoid that by checking in online - then she already has a boarding pass when she comes to the airport.