How to put drop down list of content type page in to another content type pages
YOU should use the entity reference module for the above purpose.


  Provides a field type that can reference arbitrary entities:
  
  A generic entity reference field Four widgets: Two implemented on top
  of the Options module (Select and Radios/Checkboxes), Two autocomplete
  widgets (one with one text field per entry, one tag-style with
  comma-separated entries in the same text field) Two formatters: A
  "Label" formatter, with optional link that displays the label of the
  referenced entity (the node title, the user name, etc.) A "Rendered
  entity" formatter, that renders the references entity using a
  configurable view mode Integration with Views (for both forward and
  backward references) Integration with Entity Metadata (and as a
  consequence with Search API and the like) Integration with Devel
  generate Integration with Feeds and Migrate (>= 2.3) for painless data
  import This modules depends on Entity API and CTools.
  
  Modules extending Entity reference functionality:


Earlier answer deleted following comments :
If you want to use the existing field then just go to manage fields tab under Home » Administration » Structure » Content types » A and use existing field option where you will get the existing field of other content type
Check the image below for existing field option :


Or else you can do it in the following way :

You can get your dropdown list for content type in $form_state['values']['your_field_name_for_dropdown'] and 

and Save that value in $_SESSION['module_name']['your_field_name_for_dropdown']
After saving that value you can use that value to insert into another content type in the hook_form_alter function or your custom_form itself.