My company has asked me to research Bitcoin as a potential back up storage of a slush fund due to the ease of sending money to people around the world on the field even in hard to reach locations.
I'm confused is the 51% solved or is it still an issue?
It's not really an issue that can be "solved" per se. Bitcoin's use of proof-of-work is the best solution so far, but it is not immune to 51% attacks. Double-spend attacks have occurred (by miners) in the past and it's prudent to expect that they might happen in the future: never accept zero-confirmation transactions and consider waiting for a multiple confirmations before releasing goods.
And it's probably more prudent to think of it as a 33% attack (selfish mining), and 25% of the hash rate will make the attack work a good deal of the time. Bitcoin incentivizes honest mining, but miners can act fairly anonymously if they choose to and they are motivated by profit, not goodwill. So act accordingly. Having said all that, Bitcoin is the most secure payment network in the world. Just don't accept unconfirmed transactions for payment.