ssl url rewrite in F5 ?

Typically best practice is to use URL redirect, which in-turn tells the client to come back with enctrypted url. This way it supports the HSTS also.

You can achieve this by configuring two VIPS and select the irule

_sys_https_redirect

when HTTP_REQUEST {
       HTTP::redirect https://[getfield [HTTP::host] ":" 1][HTTP::uri]
    }