grant update on table to user not working ORA-00942: table or view does not exist

I am trying to grant update rights to certain tables existing in schema TEST1 to another schema TEST2 as below

grant update on TEST1.TABLE1 TO TO TEST2;

but when I try to update TABLE1 from schema TEST2 as below

update TEST1.TABLE1

SET........................................

we get the error

ORA-00942: table or view does not exist

Please assist.