Old TM data to new installed macbook
If I recall correctly, Time Machine will notice if there are existing backups on the disk you select and ask if you want to reuse the old backup data.

I haven't tried personally but looks like you can use the tmutil command to inherit a backup, too:

sudo tmutil inheritbackup /path/to/backups


See also:  http://pondini.org/TM/B6.html