Verified answer

You can write whatever you want; it's publishing that's the problem.

Following on from Occulty's answer, in 1966, copyright in most countries other than the USA lasted for the author's life plus N years, with N typically equal to 50. Many countries have since raised it to 70.

So even if Forester's work is out of copyright in the USA, it's probably still in copyright in most other countries. That means you'll need the permission of the copyright owner (probably Forester's estate) to publish it in those countries. You're unlikely to get such permission unless you're already a well-known author. If you publish anyway, the estate will sue you when they find out.

If you don't care about making money, you can upload your book to a fanfiction site without worrying about getting permission. Strictly speaking, you're still supposed to get permission, but most copyright owners are smart enough to know that suing their biggest fans doesn't make for good publicity.

You can write a book based on the characters in The African Queen, but remember, she sank, so it wouldn't be the African Queen, but a ship named in commemoration of her. You should check if the copyrights are current on the original story.

C. S. Forester is the author of the book The African Queen. Forester died in 1966 and I find no record of his copyright in the US copyright website

http://cocatalog.loc.gov/cgi-bin/Pwebrecon.cgi?Sea...

I think you can, but you might need to do a little research of your own on the subject if you think you have a story in mind that's sellable.