You Do Need power plug adapter while traveling from Azerbaijan to Liechtenstein.

Here is Why You Need An Adapter

The outlet and plug type used in Liechtenstein are C and J and in Azerbaijan are C and F. This is how they look like.

Azerbaijan

In Azerbaijan, outlets of type C and F are in use.

Type C

Type F

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J