This feature is called Authorized Delegate.
To have the ability to enter expense reports, withdraw expense reports, etc. for other individuals do the following:

Authorization Preferences (Self-Service Delegate Assignment)
Users can now maintain their own list of authorized delegates in the Expenses Preferences page. An authorized delegate is someone who has the authority to enter expense reports on another user's behalf. This feature existed in previous versions of Internet Expenses as a system administrator task only. The ability for system administrators to define authorized delegates still exists.

Choose Responsibility
Internet ExpensesàNavigate to the Expenses PreferencesàChoose the Authorization Preferences Link

Expenses Entry Delegations
The people in this list can enter expense reports for you. They can also view all of your previously submitted expense reports. Expenses Entry Delegations can be granted by you to another person

Expenses Entry Permissions
You can enter expense reports for the people in this list. You can also view all of their previously submitted expense. Expenses Entry Permissions must be granted to you by the other person (You cannot grant your own Expense Entry Permissions).

OR

Prior to this functionality, Authorized delegate permissions were granted as follows. This functionality still exists.

Choose Responsibility    
System AdministratoràNavigate: SecurityàUseràDefine

Query up the user who is going to be an authorized delegate.

Go to the Securing Attribute regionàAdd a row

Securing Attribute ..: ICX_HR_PERSON_ID
Application ………...…: Self-Service Web Applications
Value …………………….: Choose the employee name from the list of values for the employee for which
…………………………………this user needs to be able to enter expense reports form. Bounce Apache Server
…………………………………and Clear Server Cache if Authorized Delegates are updated using this method.