How to resolve the transporter conundrum in a FTL spaceship?

Imagine a spaceship capable of achieving faster than light travel uses several transporters to allow crew members to move around its interior at the constant speed of light. What happens to the crew using the transporter when the spaceship goes to warp 2? BTW warp 2 means twice the speed of light in this context. Is there a clever way to work around this issue or I need to update the operation manual correcting warp 2 to move only at 20% speed of light?

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How to resolve the transporter conundrum in a FTL spaceship?

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