Voicebox transplants could be carried out in the UK in the next few years, according to a surgeon involved in the latest procedure.
Professor Martin Birchall said the success of the transplant in the US was "wonderful" but had involved "not much sleep" for surgeons over the course of three days.
He predicted similar transplants would be carried out in the UK shortly but said work was also ongoing in the lab to create a larynx from tissue.
Prof Birchall, an expert in laryngology from University College London, said: "We are really pleased with the success of this operation.
"We have been researching this for around 15 years and have done a lot of work in the lab on getting nerves to work again.
"To be able to do this in a human is wonderful."
Prof Birchall said the procedure was technically challenging and was suitable for only a very few patients.
"This is never going to be a common procedure," he said. "It's an enormous undertaking, it's just about the most difficult operation you can do."
He said the larynx had more fine muscle fibres "than anywhere else in the body" and had a range of complex functions, being involved in breathing, speech and eating.
"It's about the most complex organ you can repair," he said.
Prof Birchall said the UK could start screening patients for the operation within a year, subject to ethical approval.
This would create a hub for other countries, with potentially three or four transplants per year.
At the same time, work is ongoing with tissue in the lab to create a larynx, with the hope donor transplants could be replaced by tissue engineering.
In the latest operation, Prof Birchall worked closely to ensure the donor organ was removed correctly, and played a key role in repairing nerves.
He said the operation was more complex than the previous one carried out in Ohio because it involved transplanting much more tissue than before.
It is also the first time both the larynx and trachea have been transplanted at the same time.
During the procedure, the entire larynx, thyroid and a lengthy section of trachea were retrieved from the donor.
The larynx was tested with a saline solution to ensure it worked properly and would allow good blood flow.
At the same time, surgeons in an adjacent theatre removed Ms Jensen's damaged larynx and prepared her body for her new organ.
The procedure involved connecting five nerves, three arteries and two veins in complex microsurgery.
If the transplant had failed then the larynx would have been removed and not replaced. Ms Jensen would have been no worse off, according to the surgeons.
Prof Birchall said: "The operation was technically extremely challenging.
"Most of it went better than we could have hoped but getting out her larynx because of all the scar tissue was very difficult."