I don't have the native Flash files and neither does the client, we're going to have to use the .swf files off the server. I've searched and found there is software available to convert .swf files to .fla files. I've been creating my own files in Flash-- this is a first for me where I need to get in and update another designer's files. Can .swf be converted in Flash or do I really need this extra software? Has anyone had a good experience and can recommend one conversion software over another?

A SWF is a COMPILED flash file, not even Flash can UNcompile a SWF to turn it back into an FLA file.

There are many decompilers out there, but I haven't found one yet that decompiles and brings everything back as a FLA file EXACTLY as the original was created. Some won't decompile actionscript. Some turn a tween into a frame-by-frame animation, it varies.

Flash definitely cannot convert SWF to FLA and the converters don't usually do what you would hope they would do. Honestly I would just recreate the flash from scratch so you have the working files. Obviously this may not be worth it depending on the complexity of the flash but from my experience you are only going to waste time and get headaches trying to convert the SWF to FLA.