It's not difficult, but real easy to get yourself flustered and confused as to which server/database your'e working with.
so.................Backup, backup, backup.
Open PHP MYadmin on the site you wish to export. In the left column, highlight the correct database.
In the large column (right), along the top choose the operations tab and make a copy of the database (copy database to), and give it a new name.
Copy the database and structure.
I like to give it the same name but append '_copy' to the end.
To save making any schoolboy errors, lets play with the copy.
Back to the left column and highlight the newly copied database to show all the tables.
In the large section again, you can arrange by Rows.
If all you want is the stock inventory, then the tables you want should be high up the list, anything really to do with category, inventory, and options.
Alternatively, just scroll through the list and click the checkbox on anything that mentions inventory, options and category.
Make a note of the table names, write them on a scrap of paper.
Right at the bottom is a drop down box, find that and choose export, save this as an sql or CSV. I find sql best.
Importing is similar.
On the server you wish to import into.
Backup, backup, backup. (as above)
Only this time we want to work on the database, not the copy you just made. (we made this just incase we mess up)
ITS IMPORTANT THAT YOU MADE YOUR BACKUP AS THE NEXT STAGE IS IRREVERSABLE
The list of tables you scribbled down, click the checkbox against each one, find that drop down box and choose 'drop'
In the tabs along the top, choose the import tab, and import the sql file you exported earlier.
Any issues, you can use the operations tab to rename the backup you just created.