Application-theory question > exchange data between 2 sites

Hi,

I have a table users wich the users can edit and save if they are login.
Now if this user is making an transaction(air-flight) they go to a
different url (partner). What is the best application-theory the submit
the users-values such as name, surname ect into the partners-formfields?

example
1)website a: > login
2)website a: > select flight > submit
3)website b: > select airliner + times
4)website b: > fill in the required form-data (name, surname,adress ect)

If they are in step 4, the form-data is filled in by the database of
website a…

Is this possibly…or better what is the solution the exchange data
between 2 applications.

Grtz…remco