Match vertical and horizontal values and return value

Hi experts, looking for some help which hopefully you'll be able to give.

I've got a large spreadsheet which contains two sheets: Names & Group Competence (example attached). The Group competence sheet lists the level of competence of the group as a whole against a range of activities (i.e. High, Medium, Low). The Names sheet lists all of the team members and what group they are a part of (Cols A & B respectively). What I need to do be able to do is, for each group member, show the level of competence the group they are a part of has against each activity. I've highlighted the cells that I need to populate in yellow in the attached. I've tried using index / match but can't for the life of me work it out and keep getting a #REF error.

The format and structure of the data is given to me and unfortunately it can't be changed.

Any help greatly appreciated.

From a very grateful Level 1 Excel amateur

Is that what you want?
Done with PowerQuery

Thanks Ali, that works a treat! Really appreciate it - saved me loads of time

Thanks Sandy, that's exactly what I'm looking for. The dataset I have is very large (7000 rows and 150 columns) so the formula I've kindly been given on here doesn't appear to work and gets to a certain point before it crashes so I'm in need of something more efficient. Whats Power Query?

In short, PowerQuery (add-in for Ex2013 Pro Plus) is designed to transform BigData
I suggest to read it first: Getting Started with Get & Transform (PowerQuery)