Steve, if this is a one time instance, you can do this via the database.
ow_base_avatar - is the database table you need.

1. Find your user's ID. For example userID=4. ( you can find out what is your userID in ow_base_user table)
2. As any other test ( for example userID=5) user upload desired avatar.
3. Go to ow_base_avatar table, find user with ID=5. Copy his hash ( set of numbers, for example hash=1365670484).
4. Go to ow_userfiles/base/avatars, find all ( there will be several of them) avatars that end with "1365670484".
They will look like: avatar_big_5_1365670484.jpg
Download and rename them to:
for example:  avatar_big_4_1365670484.jpg  ( where #4 is the userID to whom you would like to assign new avatar)
Upload them to the server.
5. Go to ow_base_avatar table again, find userID=4>>edit>>replace his hash with 1365670484.