I know that my mother will be fine after reaching there, she is a person who knows how to adapt very easily.
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The most obvious answer is adaptable, and adjective for someone who is able to adapt quickly and are good at it. Credit for @mRotten for mentioning this first in the comments.
Versatile is also a word, though it doesn't just describe something that can adapt quickly. It can also describe something that has a lot of different things to offer.
A noun that might fit is chameleon, though it mostly refers to people who are often change their behavior, beliefs and/or facade, to fit into a situation or please someone at that moment.
One suggestion that means a person who "adapts easily" is one who is "flexible".
Without knowing more about your mom and her situation, it's only a guess as to what will fit here:
Easygoing - A person who is usually relaxed and in good humor - even when those around them may not be. Someone who "rolls with the punches". https://en.oxforddictionaries.com/definition/easy-going
Resourceful - The ability to obtain what you need and want on your own - not necessarily having to depend on others. https://www.merriam-webster.com/dictionary/resourceful
Two-faced - Able to control one's personality in order to be perceived favorably by conflicting or opposing persons - as well as allies. https://www.urbandictionary.com/define.php?term=two%20faced