The phrase "allowed them to take" is correct and usable in written English.
It can be used when discussing permission granted to individuals or groups to acquire or obtain something.
Example: "The new policy allowed them to take additional vacation days without penalty."
Alternatives: "permitted them to take" or "granted them the ability to take".
Suddenly, the Devils stopped doing everything that had allowed them to take the 3-0 lead.
But then "turned sulkily" away from the next two deliveries and allowed them to take their course.
For speed, they could switch to another mode that allowed them to take nearly 200 images per second.
Institutional investors, led by people like David Swensen it lead to a more benign interpretation of the prudent person rule, and allowed them to take chances.
Though they made up a relatively small portion of the immigrant population, their outspoken activism allowed them to take on a disproportionately large leadership role.
Ms. Pasqualini said counselors regularly warned inmates of impending drug tests or allowed them to take urine cups into bathrooms without supervision.
Thousands have migrated westward to seek a better life, particularly as the expansion of the European Union has allowed them to take advantage of freedom-of-movement rules.
Deeper pockets did not make the seas where they were tossed for hours less dangerous, and it has not often allowed them to take a room.
All the printed material we made was enriched with augmented reality technology, which allowed them to take their audience on a 360-degree interactive tour of Istanbul.
Barbecue aficionados, the couple says R.V.'s have allowed them to take their love for hot pepper sauces to a new level.
As Steve Hansen said, in the second period his forwards had an urgency and desperation about them that allowed them to take control of the match.
