Does the phone company have the right to extort funds by refusing to release the line?

While your situation is certainly frustrating, the conduct does not rise to the level of criminal extortion, in my view.

If you have hit a roadblock in the negotiations, consider hiring a lawyer to write a letter to the company on your behalf. Just as you use your doctor office to negotiate with your medical insurer, use your lawyer to negotiate with your vendors on your contract problems.

Check with a lawyer in your locale to discuss more of the details.

Good luck to you.

God bless.

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