That's fine. Alternatively, you could use "improve their awareness".
I'm writing an essay and I'd like to say: 'increase their awareness' but I've already used the word 'increase' in the previous sentence. Is it ok to say 'raise their awareness'? Here's my sentence: 'People should increase/raise their awareness of everyday life in countries of the third world.'
That's fine. Alternatively, you could use "improve their awareness".
I'm not a teacher of English, but I have spoken it for (almost) all of my life....