Store information from hook_form_alter to be used in later hook_user_update? I have a hook_form_user_profile_form_alter (hook_form_FORM_ID_alter) where I'm capturing user information that was changed when a user updates their profile.

I want some of that information available in hook_user_update, which is called after the form alter - maybe no more than 6 fields.

Is there a way to hold some of the information from the hook_form so it is available when I get to hook_user_update? I'm looking for a server side solution. In Java I could use class variables or session storage. I see PHP has session storage. Is that the best practice or is there's a Drupal specific solution or a better PHP usage pattern?

Since someone will probably ask why I don't perform what I need done in hook_form_user_profile_form_alter:
That function gets called twice (which can be problematic) and I cannot be sure that the transaction is complete until I get to hook_user_update. So I feel that hook_user_update is a much better place to execute what I need to execute, because I'm synchronizing information with another application. I need to be sure the transaction went through before I perform the call to the other app.
As far as I'm aware, all form element values entered by the user on the profile edit form are available in the hook_user_update()'s $edit argument. The only element that won't be there is the plain text password.

There is no "drupal way" to avoid this, as core handles this functionality and it's trying to stop you from accessing the plain text password.

REMOVING SUGGESTION PER @znerol. Will update later this evening