When we left Polycarp, he had honored men who were martyred recently such as Ignatius. Ignatius was a colleague, and his death would greatly shake both Polycarp and the Philippian church.
He moves on to grief over Valens. Apparently, he was a presbyter/preacher/elder, who left the church because of fear of persecution. He could not stand the thought of facing wild beasts. He clearly was excommunicated. Polycarp gives advice that I believe matches Paul's advice in 1 Corinthians 5 and then later in 2 Corinthians. Do not count such as enemies, but call them back. You may perhaps save them and the whole body. There should be a degree of shunning, but there should also be an open line of communication should he repent and seek rehabilitation.
According to Polycarp, Philippi knew Christ before Smyrna. It had a church first. "Ye are well versed in the Sacred Scriptures; nothing is hid from you; but to me this privilege is not yet granted." Paul wrote Philippi with an authoritative letter. Smyrna only received a part of a chapter in Revelation via John. Polycarp gives the constant call to pray for all people: saints, kings, potentates, princes, those that persecute and hate you, and enemies of the cross. All should receive prayer.
He also confirms that he intends to carry a letter from Philippi to Syria at the request of Ignatius. He also mentions Crescens and his sister. Crescens transcribed his letter. That is the end of his letter to the Philippians.