This link may be of interest.
[2.0] Mosquito In Service / Foreign Users
The following is a quote from the site, I changed a few words at the start but the full story is on the site. I think we can say that the US liked them.
In late 1942, a B.IV Mosquito was given to Colonel Elliot Roosevelt, the American President's son and commander of a USAAF reconnaissance squadron in North Africa, equipped with Lockheed F-4 Lightning reconnaissance aircraft. The B.IV was faster and had much longer range than the Lockheeds, and Elliot Roosevelt began to press for adopting the British machine.
In the meantime, Mosquitos were finally beginning to roll off the production lines at de Havilland Canada in the Toronto area, and in December 1942 Geoffrey de Havilland JR brought one of the first Canadian Mosquitos down to Washington DC. Hap Arnold ordered that airport traffic be held off for a half hour to allow de Havilland to put on an aerial demonstration over the city. Geoffrey De Havilland then left for California to perform more demonstrations. He went by train in order to see the country, and the Mosquito went separately. In Los Angeles he met with his cousin, actress Olivia de Havilland.
Hap Arnold now became very determined to get his hands on the Mossie, beginning with a offer to swap P-51 Mustangs for Mosquitos. The British turned him down. The Mosquito was increasingly seen as difficult to replace. Had Canada been producing Mosquitos in volume at the time, the Americans might have been able to get their hands on part of the production, but the Canadians were slow to ramp up, with only 90 Mosquitos built there in 1943. At least Arnold's persistent lobbying to get Mosquitos helped convince Bomber Command that they had something of value.
The Americans did manage to get their hands on a relatively small batch of Canadian aircraft. The US signed an agreement with the British government in October 1943 for 120 Canadian-built Mosquito bombers, but limited production meant that the US only got 5 B.VIIs and 35 B.XXs. They were converted to a reconnaissance configuration with US-built cameras, redesignated "F.8", and sent to the UK for service with the USAAF Eighth Air Force.
The F.8's camera suite was minimal and the single-stage Merlins really didn't provide the performance the USAAF wanted, and so the F.8s were eventually replaced by PR.XVIs. The Americans obtained over a hundred PR.XVIs, along with a handful of T.IIIs for conversion or continuance training.
American pilots converting from their Lockheed F-4 and F-5 Lightnings, which had "handed" propellers, had to be trained to deal with the Mosquito's tendency to roll against the rotation of its propellers on takeoff. There was a worse problem in that over-anxious fighter pilots tended to mistake Mosquitos for Messerschmitt Me-410s, which in fact did have a similar configuration, and so the USAAF gave their PR.XVIs red-painted tails as a recognition aid.
The majority of the Yank PR.XVIs were used in their intended photoreconnaissance role, but a good number of them were used for weather reconnaissance, and they were also modified for special tasks. Some were fitted with US-built "H2X" targeting radar, the American three-centimeter counterpart to the British ten-centimeter H2S, mounted in the nose radome. As American crews referred to H2X as "Mickey" for some forgotten reason, these were known as "Mickey Ships". Some USAAF Mosquitos were fitted out for dispensing chaff, and seven were fitted with communications gear to support Allied agents and resistance forces in Occupied Europe.
USAAF Mosquitos were also fitted to use the LORAN navigation system, the American answer to Gee, and as LORAN was something of an Allied standard later in the war it is plausible that some RAF Mosquitos had LORAN receivers as well.