The phrase "allow him to construct" is correct and usable in written English.
You can use it when giving permission for someone to build or create something.
Example: "The committee decided to allow him to construct the new playground in the park."
Alternatives: "permit him to build" or "let him create".
He carved out enough football and men's and women's basketball games from the ESPN and Fox deals to allow him to construct his six rivalry-based cable networks.
Brindley, however, after reconnoitring the route, persuaded the duke to allow him to construct a gravity-flow canal crossing the Irwell valley on a viaduct carried on arches.
Engelhardt had two other weather stations on the glacier, and he was eager to download their data, which would allow him to construct a precise record of fluctuations in the local climate.
Along the way, Mr. Morahan has benefited politically, allowing him to construct a reputation as a man who gets things done for people, regardless of their politics.
Mr. Kurniawan was able to provide him with access to rare, old bottles that he might never have been able to try on his own, benchmarks that allowed him to construct an intellectual history of Burgundy.
Trott praised Prior's heavy hitting at the top of the order, after the wicketkeeper-batsman had been under some scrutiny following back-to-back ducks since his surprise World Cup call, for allowing him to construct his innings, which included six boundaries from 126 balls, at his own metronomic pace.
His superior understanding of a diversity of philosophical texts allowed him to construct one of the most remarkable syntheses in medieval culture.
He learned on the job as a builder's assistant and acquired the skills that allow him to renovate the often poorly constructed houses in the favela.
Madero asked the commander of the city's garrison to surrender but the latter refused, hoping that the fortifications he had constructed would allow him to defend the city until reinforcements arrived.
Authorities have linked Breivik to Christian fundamentalism and say that he rented a farm, which allowed him to order fertilizer to construct homemade bombs.
Murray, the fiction: Griffiths jokes that Murray was a fictitious sidekick for him in creating the show, allowing him to second guess what this construct "Bill Murray" would do in a given situation.
