Yes, but if the studies were really independent, it would be kind of a waste. You can use all the data and consider the studies in one model, or you can use the second study to test the validity/reliability/reproducability of the results/conclusions from the first study.

In my estimate, the way exercised in the study proves the validity/reliability of your data gathering tool (maybe a questionnaire or an android-based app and so on). As a matter of fact, if both first and second samples are independent they can be used to analyze a common model, concurrently.

I agree with Jochen Wilhelm and Ebrahim Bonyadi , above. The two sampling approaches agree with each other, so you can put them together and treat them as one sample.

Alternatively, if the data-gathering was somewhat different (different recruitment method, questionnaire format, different cohort, response medium) then you have evidence for the consistency of your instrumentation or other aspects of your research.

But, just to be clear, we should be cautious about inferring that our measures are "valid" just because we get a similar result. I'm using "valid" to mean that you have measured what you claim to have measured. Similar results mean that the result is consistent, or reliable. Reliability is a necessary condition for validity, but not the only condition.

"Validity" can be confusing, because we use it in many different contexts. For example, we could claim that we have a "valid" questionnaire because it gives similar results to another questionnaire in a different format, even if the questions themselves do not do what they're supposed to do. We have a "valid" sample because it contains a reasonable cross-section of our target population.

When we claim to have a valid measurement because it gives similar results on two occasions, or in different formats, then we're usually talking about "internal validity", which is mostly "consistency".