why did Paul write to the Philippians?

Paul did not. God wrote to the Philippians. God used Paul as his vehicle to give the message to the Philippians. Every word from his mouth was from God.

Paul had founded the church in the city of Philipi and been its pastor for a time several years before that. He retain a close relationship with those Christian after he moved on to minister elsewhere.

In the year 62AD, Paul was arrest and send to Rome. There he spend several years under house arrest in Rome awaiting a trial before the Roman Emperor Nero. During that time Paul was unable to work but still had to purchase food, clothes, pay rent, etc.

The church at Philipi helped Paul by sending him a large offering to help to meet his expenses while he was under arrest. He responded to that gift by writing back to them (and the Colossians), give them details about his situation, encouraging them to hold on to their faith, and thanking them for their gift.

Philippians was a "thank you" that Paul wrote to his friends and supporters in Philippi to thank them for their gift.

Paul wrote to the Philippians to ask them to send their recipe for unleavened bread.

controlled by the romans , it became the first chrsitian province in europe , he was in prison when he wrote

Because he was a false prophet!

He was bored.