Create an IAM role with S3 access in Account B and set Account A as a trusted entity. Create another role (instance profile) in Account A and attach it to the EC2 instances in Account A and add an inline policy to this role to assume the role from Account B

Add a bucket policy to all the Amazon S3 buckets in Account B to allow access from EC2 instances in Account A

Create an IAM role (instance profile) in Account A and set Account B as a trusted entity. Attach this role to the EC2 instances in Account A and add an inline policy to this role to access S3 data from Account B

Copy the underlying AMI for the EC2 instances from Account A into Account B. Launch EC2 instances in Account B using this AMI and then access the PII data on Amazon S3 in Account B