The phrase "allow him to achieve" is correct and usable in written English.
It can be used when discussing granting someone the opportunity or permission to reach a goal or complete a task.
Example: "The new training program is designed to allow him to achieve his full potential in the workplace."
Alternatives: "enable him to succeed" or "permit him to accomplish".
And Mr. Romney has resisted offering many details about the cuts to government spending that would allow him to achieve the kind of deficit reductions he has projected considering the cuts in taxes that he has talked about.
Holyfield said he believed a victory could give him a shot at a more prestigious title that would allow him to achieve his goal of retiring as a heavyweight champion.
The principal reason Pietersen left South Africa for England in the late Nineties was because he did not feel the system there would allow him to achieve his goals.
And he has resisted offering many details about the cuts to government spending that would allow him to achieve the kind of deficit reductions he has projected, considering the tax cuts he has discussed.
I'm sure he is now attempting to persuade the SFA to allow him to achieve outright control".
Yarrow tells us he is always looking for the perfect combination of angle, light and composition that will allow him to achieve his goal of "one moment of excellence".
Britten, too, allows him to achieve a tragic dimension.
Cynics will say that nothing Oliver does is without a knock-on commercial advantage but he is unrepentant about what success has allowed him to achieve.
It had allowed him to achieve "true progress" in developing Taiwan, impossible on the mainland because of "subversion" and civil war.
Inness's increasing control over spatial relations, scale, drawing, and colour allowed him to achieve a sense of the idyllic and tranquil in his works.
As a young researcher, Dr. Keeling built instruments and developed techniques that allowed him to achieve great precision in making such measurements.
