With a NAT rule, or static
match destination A.A.A.A/32
then destination-nat pool etc.
An IP does not need to be configured on your public interface in order for you to use it for DNAT, the public range does need to be routed to your new public IP address by your ISP however, which I suspect is not happening.
You will need traffic routed to your SRX, since you own those IP's.
You will need a destination NAT/Static to translate the public IP to private.
You will need a security policy to allow the source (probably "any") to the real post-nat Ip of your server, likely from untrust to trust.