Well, the reward are not related with the crypto wallet.
To get your rewards from the previous pc, you must go in brave://rewards/, click the engine in the blue part, and there’s an option that’s called like “security copy”, and you will also see the recovery part, from the old pc you will make the process to make the copy, which will give like a seed, and in the new one you will make the process of recovering.
Two things before you do that:
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I warn you that if you made any BAT’s in the new one, all of that will be replaced with the old data, It won’t be added, you can see some posts here of people making the process without knowing this.
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The other thing is that I don’t really know if the estimated rewards will also be synced, maybe @Mattches or @eljuno could help us with that info.