In the article he makes the claim that Luke was the amanuensis (secretary) of the Pastoral Epistles. He bases this on 3 divisions of increasing complexity
- Luke is the only person with Paul when he wrote his second letter to Timothy
- Pseudoepigraphia would not include certain comments
On the second point the request to bring cloak (2Ti 4:13) would not be included by an anonymous author writing that Paul though he may die soon, knowing that Paul had in fact been martyred. This statement also authenticates the dating of the Pastorals.
Further, certain posthumous comments would be in very poor taste such as Paul stating he hoped to come to Timothy soon (1Ti 4:13) if Paul was in fact, by the time of writing, deceased.
Moule suggests Luke had greater leeway in the composition than I think likely.
He also suggests that Luke collected the other Pauline letters after Paul's death and compiled them into a single volume. This could explain why the Pastorals were not initially included the collections of Paul's epistles.