First, we have no evidence whatsoever for this claim. This is not based on any historical data at all. By contrast, the resurrection hypothesis has much historical evidence.
Second, this theory contradicts known evidence. Specifically, it wouldn’t account for the empty tomb (see “Empty Tomb”) or the disciples’ sudden and dedicated belief in the resurrection—despite having every reason not to (see “Expectation for the Resurrection”). This also wouldn’t explain why someone like Paul would become a Christian (see “Eyewitnesses”), because a twin brother wouldn’t be evidence enough for him to stop his quest of persecution. This historical data are simply not explained by a twin brother.
Third, the identical twin would need to want to impersonate a man who was just brutally tortured and murdered. What would be the motive for wanting to impersonate Jesus, when both the Roman and religious authorities would want you dead?
Fourth, the identical twin would need to mimic the wounds of Jesus. He would need holes in his hands and feet, and a gash between his ribs (Jn. 20:25-28). This would need to happen in a short period of time, while at the same time still convincing the disciples that he was immorally raised from the dead.
Fifth, this identical twin would need to know everything about Jesus’ life and ministry. After all, Jesus continued to meet with his disciples for 40 days after he purportedly rose for the dead. During that time, this twin would’ve needed to convince his half-brother James (1 Cor. 15:7) and his other brothers (1 Cor. 9:5), all of whom were skeptics (Mk. 3:21; Jn. 7:5). He would’ve needed to convince his mother (Acts 1:14), who would’ve known if she had twins (!!). He would have also needed to convince the various other disciples—up to and including 500 different people (1 Cor. 15:6).