Is it true that stratosphere is warmer in the top and colder on the bottom?

The stratosphere lies above the tropopause, extending to a height of about 50 km (Lutgens 20). The stratosphere is characterized by a strong temperature inversion, as shown by the above figure. This is a stable layer with little mixing. As a result, pollutants and other particles may reside in the stratosphere for many years.

A large concentration of ozone (O3) is found in the stratosphere, with a maximum concentration at about 25 km. This "ozone layer" absorbs much of the ultraviolet radiation emitted by the sun. Heat is released as the UV is absorbed, which then heats the atmosphere. This explains why temperature increases with height in this layer. (Ahrens 15)

It is interesting to note that the inversion continues beyond the maximum density of ozone. The reason for this is that much of the available UV radiation is already absorbed by ozone above the level of maximum density. Therefore, there is less potential UV that can be absorbed, resulting in lower temperatures near the bottom of the stratosphere.

The stratopause lies above the stratosphere, and like the tropopause, temperature remains constant with height. At the stratopause, the pressure is only 1 mb! This means 99.9% of the atmosphere is contained in the stratosphere and troposphere. Yet the atmosphere continues upward: 99% of the remaining mass is found in the mesosphere and 1% in the thermosphere (Wallace and Hobbs 24).

It's lithogenous i believe of course i looked it up.