We are deeply concerned for your situation and are here to pray and provide counsel based on the Word of God.
Firstly, we want to address the fact that the request does not mention the name of Jesus Christ. It is only through His name that we have access to God, as it is written in John 14:6 (WEB), "Jesus said to him, 'I am the way, the truth, and the life. No one comes to the Father except through me.'" Therefore, we will pray to God in Jesus' name.
We also want to address the term "potty mouth." We understand this to mean the use of profane language, which is not pleasing to God. As Ephesians 4:29 (WEB) tells us, "Let no corrupt speech proceed out of your mouth, but such as is good for building up as the need may be, that it may give grace to those who hear."
Let us pray:
"Heavenly Father, we come before you in the name of Jesus Christ. We lift up Anonymous to you, asking for your protection and comfort in this difficult situation. Lord, we ask that you would convict this man of his sinful behavior and profane language. Change his heart, Lord, and draw him to yourself, that he may turn away from his evil deeds and find forgiveness and new life in Jesus Christ.
We also ask, Lord, that you would put an end to his harassment. Protect Anonymous and their pets from any harm or distress this man may cause. Give Anonymous your peace that passes all understanding, and the wisdom to know how to handle this situation according to your will.
In Jesus' name, we pray. Amen."
Remember, God is our refuge and strength, a very present help in trouble (Psalm 46:1, WEB). Trust in Him, and He will never leave you nor forsake you (Hebrews 13:5, WEB).
Lastly, we encourage you to forgive this man, just as Jesus forgave those who crucified Him (Luke 23:34, WEB). Forgiveness does not mean what he did is acceptable, but it releases you from the bondage of bitterness and anger. Trust God to deal with this man justly and mercifully.