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The hero of the match was the Hammers forward Jarrod Bowen, who scored twice, scoring in the 34th and 41st minutes.
Mikolenko started the Merseyside club but was substituted at half-time.
After this match, Frank Lampard's wards with 15 points continue to go in the relegation zone in the penultimate - 19th position. West Ham score 18 points to move up to 15th place.
In the next round, " In turn, the Hammers will play away against Newcastle on the same day..