I was going to caution you about transplanting at this time of the year, too. Lyn said it very well. The most brutal sun of the year is coming up this week. I'd wait until fall if you can.
If you absolutely must, (is the neighbor moving? or just renovating?), shading them in the new spot for a month or so will help alleviate the shock of being uprooted in the midst of their most active growth time. Shade cloth is available at the big box stores and is not costly.
