Amazon CodeCommit に push されたファイルを S3 に自動保存したい

以下のブログが参考になると思います。 https://www.packetswitch.co.uk/how-to-use-nexttoken-in-boto3-aws-api-calls/
コードにすると以下のような感じだと思います。

# coding:utf-8
import boto3

def lambda_handler(event, context):
    commit_id = event['Records'][0]['codecommit']['references'][0]['commit']
    rep = event['Records'][0]['eventSourceARN'].split(":")[5]

    s3 = boto3.client('s3')
    codecommit = boto3.client('codecommit')

    next_token = None
    all_files = []

    while True:
        if next_token:
            response = codecommit.get_differences(repositoryName=rep, afterCommitSpecifier=commit_id, NextToken=next_token)
            files = response['differences']
        else:
            response = codecommit.get_differences(repositoryName=rep, afterCommitSpecifier=commit_id)
            files = response['differences']

        all_files.extend(files)

        next_token = response['NextToken']
        if 'NextToken' not in response:
            break

    # ファイルごとの操作
    for file in all_files:
        path = rep + '/' + file['afterBlob']['path']
        blobid = file['afterBlob']['blobId']
        content = codecommit.get_blob(repositoryName=rep, blobId=blobid)['content']
        s3.put_object(Bucket='バケット名', Key=path, Body=content)