Combine cell content

I have the following sheets:

Sheet1
A B
10 a
20 b
30 c
40 d
50 e
60 f

Sheet2
A B
a aa
a ab
b ba
b bb
b bc
c cc
d dd
e ea
e eb
f


Is there a way using excel formula to find out if a from Sheet1 column B is present in Sheet2 column A and if it's found then can i have column C in Sheet 2 as:

Sheet2
A B C
a aa a aa ab
a ab b ba bb bc
b ba c cc
b bb d dd
b bc e ea eb
c cc f
d dd
e ea
e eb

Really appreciate your help. TIA.