"rightfully claim" is a correct phrase in English, and you can use it when you are talking about someone who has a justified demand for something.
For example: "The protesters are rightfully claiming their right to free speech."
Could Mr Chaudhry now rightfully claim his old job back?
It can rightfully claim to have done some cultural reprogramming of its own.
Geocaching can rightfully claim to be one of the fastest growing outdoor activities.
Basketball soared internationally and now can rightfully claim to be the world's second-most-popular sport behind soccer.
That outfit was deemed so stylish it caused the fashion industry to, rightfully, claim Malik as one of their own.
The Pakistani asylum seekers rightfully claim they did not commit any crime and only wanted to visit Fox compound.
Edin Dzeko rightfully claimed a penalty when Ashley Williams' block cannoned into his own upheld hand.
(In fact, 68 percent of the nearly 100,000 returns on which taxpayers claimed the adoption credit were audited by mail, according to a report by the Government Accountability Office, which reviewed the I.R.S.'s strategy to ensure taxpayers were rightfully claiming the credit).
Del Tufo rightfully claimed Roth for the city and quoted a famous line from "Goodbye, Columbus": "I felt a deep knowledge of Newark, an attachment so rooted that it could not help but branch out into affection".
Until Monday, Maliki could have rightfully claimed that he should have been tasked with forming the government, since he was the leader of the April election's biggest winning group.
Though Kurt Masur rightfully claims an affinity for the German Romantic repertory and conducts it with authority, there can be an overly emphatic quality to his performances, especially of Beethoven and Brahms, as if he had something to prove.
