You should always use the same formal application and interview process for an internal hire to avoid some of the disadvantages of internal recruitment. When an internal member of a team fills a role within the organization, there is the possibility that others will be jealous, your leaders will be accused of favoritism or the team will feel pitted against each other.
You can avoid most of this by simply following your standard application and interview process. By following your typical application and interview process you will show that you are dedicated to putting the right person in the right role at the right time with equity and integrity.