If you'd bothered to read the laws of Liberty, it clearly states in the Introduction, that for the purposes of Liberty law, ALL independent systems immediately connected to a Liberty core system are regarded as the house of Liberty. Galileo is even stated as a Zone 4 system in Section Two of the legal code.
As such, the fine will stand, as is.
Ferris Dufresne is the head of the Central Liberty Internal Treasury. Need I explain more?
Until payment has been made, your base is considered illegal - However, I'm granting you a twenty four hour grace period, starting...now. After twenty four hours, your base will become a target for the Liberty Navy.