Why is it fair to inherit money? Because it's like any other inheritance.
Is it fair that people inherit good looks from their parents? Or athletic potential? Try getting to play in the NBA if you had two very short parents.
Or what about the place where you were born? Is it fair that some people are born in Germany, Sweden, or the USA, while others are born in Somalia, Afghanistan, or North Korea?
The simple fact that you inherited money doesn't mean you didn't deserve it. You deserve it as much as anything else you got by pure chance.
If you think it would be fair to "equalize" the situation by taking away the money people inherit, then there are many other situations that should be equalized as well. One could start by abolishing nationalities, allowing everyone to live and work in whatever country they wanted. Then one should abolish all professional sport competitions, no one should be judged by their sports skills. Also, what about people with inherited musical skills? Get rid of music as a profession as well...