df = df1[['username', 'date', 'time', 'duration']].merge(df2, left_on='username', right_on='username')

date  duration email phone   time username
0  2015         5              14:00       aa
1  2016        10              16:00       bb

email   phone username
0  rrr@  333444       aa
1   tt@  555533       bb

username  date   time  duration email   phone
0       aa  2015  14:00         5  rrr@  333444
1       bb  2016  16:00        10   tt@  555533

df1 = pd.DataFrame({
        'username':list('abccdd'),
         'email address':[''] * 6,
         'phone number':[''] * 6,
         'duration':[5,3,6,9,2,4],
})
print (df1)
  username email address phone number  duration
0        a                                    5
1        b                                    3
2        c                                    6
3        c                                    9
4        d                                    2
5        d                                    4

df2 = pd.DataFrame({
        'username':list('abcd'),
         'email address':['a@a.sk','b@a.sk','c@a.sk','d@a.sk'],
         'phone number':range(4)
})
print (df2)
  username email address  phone number
0        a        a@a.sk             0
1        b        b@a.sk             1
2        c        c@a.sk             2
3        d        d@a.sk             3

df = (df1.merge(df2, on='username', how='left', suffixes=('_',''))
        .drop(['email address_','phone number_'], axis=1))
print (df)
  username  duration email address  phone number
0        a         5        a@a.sk             0
1        b         3        b@a.sk             1
2        c         6        c@a.sk             2
3        c         9        c@a.sk             2
4        d         2        d@a.sk             3
5        d         4        d@a.sk             3