All you have to do is have the client request a copy of the lab results and the paramed (I always have the paramed company fax me a copy of the paramed).
Once you have the lab results and the paramed you can submit it with the apps to the other carriers. Of course, most carriers have a time limit on how far back they'll go on the lab results. Generally 90 days.
I will sometimes take an app with two different carriers and submit them at the same time and just have the nurse complete an exam for each. Works just as well.