SSRN exists for the express purpose of making working papers available, so it is a common practice for professors to post working paper versions of their articles in SSRN. Technically, once an article is accepted for publication, it is no longer a working paper but is a forthcoming article. While the distinction between a working paper and a forthcoming article is real, many professors don't pay attention to those distinctions and sometimes ask to post the edited versions of their forthcoming articles on SSRN to get them out into the world faster.
It is up to each individual Journal to decide whether to allow an author to post an early version of the forthcoming article to SSRN, but it is suggested that you make it clear that they may not post edited versions you share with authors as you work through source-gathering and cite-checking since things may change. Again, it's not a hard and fast rule and if the author is well known and insistent, you may decide to be a bit more lenient about it. But, in allowing this you also lose the ability to be the "first" to publish a piece if the author posts various edited versions of the piece throughout the editing process.
