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The Hammers sealed their place in the last eight of the competition when they defeated the League One side 1-0 on Wednesday evening.
A second-half strike from Tomas Soucek was the difference between the two teams in a game where chances were at a premium.
Kudus made just his second start since joining West Ham and played the full throttle against Lincoln City in the cup competition.
The playmaker started as a no.10 and was a lively presence throughout, even after moving to the ring wing in the second half.
In the aftermath of the game, the 23-year-old was voted man of the match following his impressive outing.
The Ghana international has already scored two goals since joining West Ham from Ajax Amsterdam in the summer.
On his first start, he scored twice in the Hammers’ victory against Backa Topola in the UEFA Europa League last week.
Kudus is, however, yet to start a Premier League game, although his impressive performances might force manager David Moyes into a rethink ahead of this weekend’s league clash against Sheffield United.