If you take the UML standard by the letter, a sequence diagram is an interaction diagram (clause 17.8 of the specs), and therefore represents interactions between elements of an enclosing classifier (clause 22.214.171.124), which means a class, a component or the system as a whole.
An actor does not belong to the system: it should therefore not appear as a lifeline. Typically, what should appear as a lifeline instead, is an instance of some classifier that belongs to the UI and that would notify the user of the information.
Therefore, this diagramming practice is formally incorrect.
Philosophical remark: a user does not offer a reliable interface and may react in an unforeseen or irrational manner to incoming messages ;-)
It is however a common and convenient practice to include an actor in a sequence diagram. After all, the UML standard sees the actor as a classifier (clause 18.1.2), although it doesn't belong to the system.
As this is not foreseen by the standard, there are no clear rules about what can be done and the applicable semantics. If you opt for this approach, you are therefore free to proceed as you want.
This is however a non standard use of UML. It can be an issue if valid UML models are contractually required in your project.
Philosophical remarks: the main interest of UML diagrams is to communicate the internals of a system. Abusing syntactic elements (e.g. actors in a sequence diagram) can sometimes improve this understanding, provided it is done in a manner that is consistent with the standard (e.g. use a classifier where a classifier is expected) and with comments where it is ambiguous. And finally, one can always argue that there is a larger system made of the modelled system and its users.