The possibility of Ephesians being an encyclical letter which therefore could argue for the epistle from the Laodicea being, in reality, the Ephesians epistle has been mentioned several times with good arguments. Dr. Robert Gromacki provides the other view that Ephesians was not an encyclical letter in his introduction to Ephesians.
“To whom did Paul write? The opening verse reads: ‘...to the saints which are at Ephesus, and to the faithful in Christ Jesus’ (1:1). However, there is a slight problem with the text here. The words ‘at Ephesus’ (en Epheso) are not found in three major Greek manuscripts: A Chester Beatty papyrus, dated about A.D. 200 (P 46); Codex Sinaiticus, dated in the fourth century; and Codex Vaticanus, likewise added from the fourth century. Because of the omission, many believe that Paul wrote this book as an encyclical letter to the seven churches of the province of Asia. This means that the Epistle was first sent to the leading church of area, Ephesus, and that after it was read and perhaps copied, it was sent on to Smyrna. There the procedure was repeated, and the letter moved onto Pergamos. The letter thus made the circuit of the seven churches, ending up a Laodicea. In his conclusion to Colossians, Paul charged: ‘And when this epistle is read among you, cause that it heard also in the church of the Laodiceans; and that you likewise read the epistle from Laodicea’ (Col. 4:16). Some have identified the Laodicean letter as the encyclical letter, known to us as Ephesians. Although no positive identification can be made, this position appears plausible. For further support that his was a general letter, it has been pointed out there are no personal greetings contained within the letter and that there is no treatment of specific local church problems. This is strange in light of the fact that Paul spent a lengthy three years in Ephesus. Also, the run usual use of the ‘heard’ (1:15; 3:2; 4:21) seems to indicate that both Paul and his readers had only an indirect knowledge of each other’s affairs. It is true that Paul was unknown personally to many within the province of Asia (Col. 2:1), but he knew very well the believers at Ephesus. This position, accepted by several evangelicals, does have one major problem: There are no Greek manuscripts that include the name of any other city in the space normally occupied by ‘at Ephesus.’ If the Epistle did make the rounds of the seven churches and if the churches were to insert their own geographical location into the blank space, then why has not at least one manuscript been found bearing the name of Smyrna or Thyatira or Philadelphia, etc.?
The great majority of Greek manuscripts do include the words ‘at Ephesus.’ The early Church Fathers wrote that the Epistle was sent to Ephesus. The omission of personal references may be attributed to Paul’s purpose in writing and /or to the purity of the Ephesian church (cf. Rev. 2:1-7).
Even if the letter was designed as an encyclical Epistle, it would appear that the book was first sent Ephesus and that it probably returned to Ephesus, that mother church of Asia, after it moved through the church circuit. In that way, it gained the title of Ephesians. In any case, the content or teaching of the Epistle is not affected by the problem of destination.”[1]
I believe that the letter from the Laodiceans was written by Paul and hand-delivered by Tychicus. Tychicus first dropped off Ephesus and then the letter to the Laodiceans. Now the letter is lost like the letter referred by Paul in 1 Cor. 5:9. Both of these letters now lost contained solid pastoral counsel from Paul that Paul expected the churches to read these and obey.
[1] Robert G. Gromacki, New Testament Survey: Baker book, 244-245.