Excel VBA find, match and append worksheet values?

I am in need of VBA code that performs the following function(s):

If any cell in Workbook 2, Sheet 1, Column B = any cell in Workbook 1, Sheet 1, Column B, then match value in Workbook 1, Sheet 1, Column A (A, B, C, etc) and enter matching result in Workbook 2, Sheet 1, Column A.

WORKBOOK 1
   SHEET 1
COL A.	COL B.
A	JANUARY
B	FEBRUARY
C	MARCH
D	APRIL
E	MAY


WORKBOOK 2
   SHEET 1
COL A.	COL B.
	DECEMBER
	JANUARY
	DECEMBER
	JANUARY
	APRIL
	DECEMBER
	AUGUST
	FEBRUARY
	FEBRUARY
	DECEMBER
	JANUARY
	DECEMBER
	JANUARY
	APRIL
	MAY
	JANUARY

Result should be as follows on Workbook 2, Sheet 1:

COL A.	COL B.
L	DECEMBER
A	JANUARY
L	DECEMBER
A	JANUARY
D	APRIL
L	DECEMBER
H	AUGUST
B	FEBRUARY
B	FEBRUARY
L	DECEMBER
A	JANUARY
L	DECEMBER
A	JANUARY
D	APRIL
E	MAY
A	JANUARY

As I am a complete novice with VBA code, I am not aware if macros can be executed to check against multiple workbooks. If not, I could always combine the data on one workbook, and use Sheet 1 and 2 - if necessary. Alternatively, I could have all the data in Sheet 1 only if that makes it even simpler.

Thanks for your time and input.