Should I upgrade the cable of my Line Conditioner?

No. Furman supplies a suitable cable. Replacing it will be a waste of money.

@xcool --

I was told that the manufacturer only supplies a power cord that is good enough to get you started until you can save enough money to buy a better power cord. Does this not hold true for the original cord that goes in the power conditioner?

If you think what you were told is undeniably correct, you probably will hear an improvement with a new power cord. But please consider the value of spending money on a dubious proposition that may cause at most a marginal difference. Would that money be better spent on acoustic treatments? On a Qobuz subscription? On a measurement mic to help optimize speaker and listener position? On a pair of concert tickets or flowers for your SO? The decision, of course, is yours to make. After trying many, I am dubious that cables are an important place to sink one’s hard-earned money.

P.S. You might find this essay (with measurements) interesting.