The first "clue" to the partnering is the list of names found in both books (Paul, Timothy, Luke, Demas, Epaphras, Aristarchus, Mark, Archippus, and notably Onesimus).
As we compare Colossians 4 and Philemon, we find that Paul sent Tychicus with Onesimus to the Colossians to "inform" them about his situation. Philemon gives Onesimus' back-story.
Furthermore, we learn that the letter Paul sent to Laodicea and Archippus is probably Philemon (since Philemon is addressed to Archippus). Paul instructs Colosse and Laodicea to share these letters with each other.
This gives some reason as to Paul's lengthy closing in Colossians 4; all of the greetings from his fellow-workers (along with his acceptance of Onesimus) gives some support for his plea to Philemon to accept Onesimus back as more than a servant (or slave).
Anyway, even though there is not a lot to "learn" through this connection, it helps to flush out what was happening in Paul's ministry and gives some insight into his letter to the Colossians.
Remember way back at the end of Week 2 we made an Overview of Colossians? Time to update!!!
My overview is just a loose-leaf sheet in my binder with the following things listed: author, recipients, setting, theme, key verse, purpose/occasion, chapter themes, and key words. If you mark your Bible, add this information in an appropriate margin or space.
Next week we will add some sections (or segments) to the overview and learn how to outline Colossians.