Here's the quiz: How would you accomplish the placement of the second beam
onto the posts if you had to be self-reliant?
You already have one beam in place so you are half way there. One method
would be to use a couple of 2 bys sistered together set vertical with one
end on solid ground and braced to the existing structure. Hang another
couple of 2 bys sistered with one end braced with a rope to a solid anchor
and the other bolted to the verticle, leaving a few feet hanging
beyond. Use a clevis or chain to hold one end of a block and tackle. Hook
off centered to the beam to be raised then lift one end. When it is near
where you want it then set that end close to where you need it and maybe
lash it in place. Raise the other end, set in place then unlash and do
final positioning. Easier to do than write about.