It is tricky to make a good connection as it does not really stick to solder. Yes, if you are patient, you can drop a lot of solder on copper tape (or other type of copper surface) and dip the edge of the SMA to connect. But, it is tricky.

Another way is to crimp a small metal bead. You can crimp it together with small wire, or solder wire on the crimp bead (if it is made of material that stick to solder), or you can make a loop to further sew with conductive thread.

Here is the instruction came with the Flexinol (SMA).

The package also contained some small metal crimp (the thin small one on the left). You can also buy a small crimp beads, which is usually sold for jewelry making.

Setp 1: Let the crimp bead go through the SMA

Setp 2: Turn the edge around and let it go through the bead. This is a bit finicky. When the edge goes through the bead, crimp the bead with pliers. Make sure to apply enough pressure to fix the wire.

Step 3: Repeat the same process to the other side, and it is ready to be connected.

Step 4: Fix the loop with conductive thread like sewing button holes. Make sure the connection between SMA and thread is tight and firm. A lot of current will go through the tread, so make sure to use good conductor thread. I used Karl Grim copper thread here.