There is no simple way to search for the same (real) user across multiple dating sites.
The idea that you would want to do this to verify consistency in the user's self-description seems to be working too hard to get an answer that doesn't help you out very much. The basic outcomes of such a search would be the following:
1) User is consistent across profiles, all of which can be found – but may still be lying about their height, marital status, etc. Consistently dishonest is still consistent.
2) User is consistent across findable profiles, but actually has several variant profiles that remain undetected (for example, profiles that change the user's gender, and/or use a significant quantity of falsified data)
3) User is inconsistent across profiles, but for "innocent" reasons – no longer active on a certain site, and profile information has changed since they last logged in (used to be married, now divorced; used to be 100K+ salary, now unemployed). The user themselves may not be aware that their profiles are not up to date – given the time required to craft a profile when joining a site, many users do not regularly update their own profile unless they experience a dramatic change in messages/replies to their messages.
4) User is intentionally inconsistent across profiles, for "targeting" reasons. Many people do not like to read or respond to profiles that are too general, or too accepting of other types of users (the woman willing to date men 18-80, the man willing to date women any distance away). By creating different profiles to target different groups they might be interested in, the user may experience improved results, and meet more compatible people… For example, a bisexual person who lists twice as gay and straight – and would be happy and monogamous in either type of relationship.
The question also implies that once your friend "likes" a profile on a dating site, they start placing expectations/hopes on that person being "the one" before meeting. This is not only dangerous, but highly unlikely to work out statistically. By placing too much energy in a single pairing, your friend risks being disappointed and having to start over – and perhaps eventually burning out on online dating entirely.
The alternative, and the path I would strongly advise, is instead to simply conduct an ongoing search, and not place all your eggs in a single basket. By either actively dating multiple people at once, or at least continuing to make contact with new potentials, your friend can better reduce the risks/pain of meeting a poor match, or having a good online connection simply sputter out after meeting.