Answer by taking a quote from the following article:

Edward Joseph Drake (16 August 1912 - 30 May 1995) was an English football player and manager. As a player, he first played for Southampton but made his name playing for Arsenal in the 1930s, winning two league titles and an FA Cup, as well as five caps for England. Drake is Arsenal's joint fifth highest goalscorer of all time. He also holds the record for the most goals scored in a top flight game in English football, with seven against Aston Villa in December 1935.

Drake moved to Arsenal in March 1934 for PS6,500, and scored on his league debut against Wolves on 24 March 1934, in a 3-2 win. Although he joined too late to qualify for a League Championship medal in 1933-34, Drake would win one in 1934-35, scoring 42 goals in 41 league games in the process - this included three hat-tricks and four four-goal hauls. With two more goals in the FA Cup and Charity Shield, Drake scored 44 in all that season, breaking Jack Lambert's club record, one that still holds to this day.  The following season, 1935-36 Drake scored seven in a single match against Aston Villa at Villa Park on 14 December 1935, a club record and top flight record that also still stands. Drake claimed an eighth goal hit the crossbar and went over the line, but the referee waved away his appeal. Drake would go on to win the FA Cup in 1935-36 with him scoring the only goal in the final and the League title again in 1937-38 with Arsenal.  Despite being injured regularly (he was a doubt up until the last minute for the 1936 Cup Final), Drake's speed, fierce shooting and brave playing style meant he was Arsenal's first-choice centre forward for the rest of the decade, and he was the club's top scorer for each of the five seasons from 1934-35 to 1938-39. The Second World War curtailed Drake's career, although he served in the Royal Air Force as well as turning out for Arsenal in wartime games and also appearing as a guest player for West Ham United later in World War II. However, Drake's career would not last long into peacetime; a spinal injury incurred in a game against Reading in 1945 forced him to retire from playing. With 139 goals in 184 games, he is along with Jimmy Brain the joint-fifth all-time scorer for Arsenal.  Drake is as well one of 32 Arsenal legends who are emblazoned in a mural upon the walls of the club's Emirates Stadium.

Did he stay with Arsenal after winning?
With two more goals in the FA Cup and Charity Shield, Drake scored 44 in all that season, breaking Jack Lambert's club record, one that still holds to this day.