In theory, yes.
In reality, Aruba and even Holland do not do enough business with Peru to warrant an extradition of someone who murdered any Peruvian citizen - let alone a popular Peruvian celebrity's daughter.
I'm sure Peru's answer will be that they will be happy to hand him over as soon as he's served his Peruvian time.
I'm guessing that Peruvian prosecutors will argue that both Aruba and the FBI had the opportunity to arrest him and convict him and they squandered their opportunities - and, as a result, he was walking around free to murder Miss Flores.
I'd add that a lot of posters here seem to think that he will suffer deeply in prison in Peru.
However, compared to most Peruvian inmates, he is fabulously wealthy. If his mother can get enough money into him to keep his fellow inmates supplied with contraband, etc. he will likely be able to buy protection. Also, at 6'3", he is young, strong and physically bigger than most Peruvians.
His time in prison will be brutal by our standards, but probably not what he deserves.
I'm guessing that Peruvian prosecutors will argue that both Aruba and the FBI had the opportunity to arrest him and convict him and they squandered their opportunities - and, as a result, he was walking around free to murder Miss Flores.
The US authorities and the FBI were not dealing with a murder case, but an extortion case. That's what the US authorities want Joran van der Sloot for.
And as far as Aruba, I don't think they want him for anything.