How to dump one hard drive on to another with an operating system on it?

1. OK. I'm assuming that the 150 GB HDD bootable drive functions problem-free at this time, right? If it doesn't meet that criteria don't read any further...

2. Since your 2 TB HDD is not data-full and can easily accommodate another 150 GB of data, first shrink the volume (partition) of the 2 TB HDD by slightly more than 150 GB - say, 155 GB. That will create that amount of disk-space on your HDD as unallocated disk-space. You're going to use that disk-space to house the SSD's 150 GB or so. I assume you know how to use Disk Management to shrink the partition.

3. Using a disk-cloning program (see Google) for a listing of freely-available programs, clone the contents of the 150 GB HDD to the unallocated disk-space you created on the 2 TB disk.

4. A couple of things to keep in mind...
A. Most, but not all, disk-cloning programs will allow you to clone the contents of your source disk, i.e., the 150 GB HDD, to a destination disk's unallocated disk-space. In some cases the disk-cloning program will require that a partition (volume) must first be created on the destination disk. Obviously you can easily meet this requirement using DM to create the partition from the unallocated disk-space.
B. In some cases the disk-cloning program will create a partition on the destination drive only to the extent of the total data contents you're cloning. There's no problem here either since you've created sufficient disk-space (unallocated for the moment) to house the total cloned data contents.

BE EXTREMELY CAREFUL BEFORE UNDERTAKING THE DISK-CLONING OPERATION. YOU DO NOT WANT A DISK-TO-DISK CLONING OPERATION WHEREBY THE PROGRAM WILL FIRST DELETE THE ENTIRE CONTENTS OF THE DESTINATION DISK (YOUR 2 TB HDD) AND THEN CLONE THE CONTENTS OF THE 150 GB DISK TO A DISK EMPTY OF DATA.

5. Following the d-c operation disconnect the 150 GB HDD from the system and connect the 2 TB HDD (which will become your new boot drive) to the motherboard's first SATA connector (0 or 1).

6. Boot to the new system and assuming all is well, ensure that the non-C: data partition on the newly-cloned 2 TB disk bears the same drive letter assignment letter it formerly had before the d-c operation. It probably will, but sometimes #!@* happens and the drive letter has been changed as a result of the d-c operation.