VBA to replace duplicate values with unique values from different column

[TechnicalBeginer]

Hello I have table like that:
1.1 Covid cases in hospitals per date. Column 6 is Hospitals with strings of the hospital names. There is like 40,000 of items.
1.2 In column 5 of this Sheet I have emty column, where the Hospitals IDs should be placed (like 40,000 items).
2. Now, in different sheet called Hospitals, I have list of hospitals, two columns. In column A I have hospitals IDs. In column B I have the strings of the hospitals, total 182 hospitals.
2.1 What I would like to do is to use these keys in column B, to compare with column 6 (Names of hospitals). If there is complete match of the string value, then copy the value from column A (from Hospitals) to column 5 (the ActiveSheet)

Can you help to do it? I am a newbie and I have no idea if is there such function in Excel 2002 or there is need to write it down as a more complex code.

 

[TechnicalBeginer]

Yet I have forget to add the point 3. On the final step I would like to replace the Strings of Hospitals in activeSheet With reference to the Hospitals! column B...