Your local dealer or independent shop.

Do you plan on doing the work yourself or are you gonna take your bike to a shop?
Do you have a fairly complete set of hand tools?
If you're gonna do it yourself the first thing you need is a Factory Service Manual.

 

On an FXR, the "box" is behind the right side cover... plug [actually unplug] and Play [with a replacement]
First and Cheapest place to start...as the module is Usually free at a friendly Indy, or even a friend who has "Upgraded"
Make sure you get the one with the same plug you have!!!
Let me say that on mine the rev limiter quit working... but on another guys ride... it was like yours is doing..

Keep riding it...and you will know,as it was Not that many more miles and it quits altogether... then you know!!!!!

 

Get lolly pops for your straight pipes. Advance the timing and rejet carb. Sure theres more, but those are cheap and easy fixes

 

I suggest we take a step back for a few moments chaps. OP lives in Portugal, so Gonçalo, we really need to know what the origins of your bike are. Many bikes in recent years have been imported from the USA second-hand, in which case the comments above are perfectly valid. However if your bike is a genuine International bike it may still have original spec parts, such as high gearing, carb, cam and ignition system, which are different to US spec bikes. Most particularly it may still have the original induction manifold, which has a restrictor in it, which will kill performance (although actually fitted to reduce engine noise). That is consistent with the limited speed you mention.

So before we go any further can you check its VIN for us please? Go to the H-D website and the Owners tab, where you can enter your VIN, which will reveal the intended market, most likely either US or International. I should add that my 1990 Evo was bought new by me here in the UK and is an International spec model, although I have discovered and removed all the International spec features, over the years.

 

Good call G

 

Bike is cutting off, as in motor stops? Then re ignites at 60mph?
Not how a rev limiter works that I’ve ever know of

 

very observant... good on ya...
Translation being everything... I'm gonna stand on rev limiter...as it stutters... [not cuts off, Granted] until speed is reduced at which point it normalizes...until you over rev again!!!
When Carbs, pipes other tuning are involved... the engine simply lays down...quits pulling...goes Flat!!! No Stutter unless really Fat...
And like I said... i doubt it was ever intended to cut off at 90MPH... therefore...it is probably malfunctioning...and on it's way Out!!

Unless we are right there...to Diagnose based on experience...we are all Guessing However... Ones mans "dies" is another mans "lays down, quits pulling"!!!!

 

That is what I am reading in his description...the engine simply quits pulling...but i am betting something is lost in translation...

 

What happens at wide open throttle in 3rd or 4th gear? Same thing at a lower speed? Nothing? Or in neutral? The speed thing is some kind of confounder here. There's no speed sensor to ignition module link. No electronic speed sensor at all on that bike. So it's more like it takes from 90 to 60 for a breaker to reset or wires to reconnect themselves at a break or something like that.

 

Bahhhm