If you need to edit a quotation, one standard practice is to put the changes in square brackets.

Well, I am not really editing the quotation. This is the original sentence in the book that I am quoting:

According to this definition, which was first introduced by Salamon and Anheier in 1992a, an organization is defined as a nonprofit entity if it shows the following five characteristics:...

So how should I do it?

Should I do it like this:

It says, "an organization is defined as a nonprofit entity if it shows the following five characteristics" (ibid:47)...

or like this:

It says, "An organization is defined as a nonprofit entity if it shows the following five characteristics" (ibid:47)...

or like this:

It says, "[An] organization is defined as a nonprofit entity if it shows the following five characteristics" (ibid:47)...

or like this:

It says that "an organization is defined as a nonprofit entity if it shows the following five characteristics" (ibid:47)...

Or should I write: It says that "an organization..."?

I think that's a good solution. Edits are hard to demonstrate here on LEO because square brackets disappear. I'll use curly brackets instead to show the principle:

Question 1. "{A}n organisation is defined as...". Discuss this proposition.

Hmm, when I write square brackets, they disappear - well, I thought so!

Test: []

Put in square brackets only what you're changing, i.e. the 'a'. Otherwise the reader would be justified in thinking that you're inserted the whole word 'an'.

That's actually the way I wrote it initially. But MS Word then suggests with its annoying green underlining to drop the "that"-word. Once I did that, it suggests to add a comma. And finally after that, it suggests to capitalize the "An".

Is MS Word wrong?

if the original sentence begins with an A, I'd put it too, otherwise begin your quote with "a

... and don't believe to much in MS Words Rechtschreibkorrektur, there are a lot of threads here dealing with this somehow stupid thingie ...

MS Word can certainly be wrong. I must however admit that I completely disable spell check, grammar check, auto-correct, auto-format, and all of these features; therefore I don't have much experience with them!

All right, that leaves me with two alternatives:

It says, "an organization is defined as a nonprofit entity if it shows the following five characteristics" (ibid:47)...

OR

It says that "an organization is defined as a nonprofit entity if it shows the following five characteristics" (ibid:47)...

Which one would you prefer?

Thanks for your excellent help :-)

I'd use the second because it runs very smoothly and requires no editing of the quotation. The first requires a capital A in square brackets at the start of the sentence and is also completely fine.