How do I merge my branchB of branchA into Master in Git?

I effectively have this:

a -- b -- c                           <-- Master
           \
            d -- e                    <-- BranchA
                  \
                   f -- g -- H -- i   <-- BranchB

What I want is to integrate my changes from BranchA and BranchB into Master. I normally like to rebase, but I don't think it's a good idea as my changes are in public repos, and in particular, commit H is someone else's work.

So if I am right in my assumption that a merge is easier, I am wondering, do I need to merge Master into BranchA, then merge BranchA into BranchB, before merging BranchB back into Master, or can I save some time and just merge Master into BranchB, then merge it all back in? I understand this will leave a messy commit history, hence my previous paragraph.

Edit:

There are changes in the master as this is a team project.

Just check out the master and merge BranchB into it, this merges all changes into master as BranchB contains all changes from BranchA.

a -- b -- c                           
           \
            d -- e                    <-- BranchA
                  \
                   f -- g -- H -- i   <-- Master, BranchB

Since this will lead to a fast forward merge, if there are no changes on the master, you might want to consider the option --no-ff that creates a new commit telling explicitly that the branch hand been merged.

a -- b -- c -------------------------- j  <-- Master
           \                          /
            d -- e                   /  <-- BranchA
                  \                 /
                   f -- g -- H -- i   <-- BranchB

Depending on what you want to "tell" with the history, you can also merge first merge BranchA first and then BranchB.

a -- b -- c -------j------------------ k  <-- Master
           \      /                   /
            d -- e                   /  <-- BranchA
                  \                 /
                   f -- g -- H -- i   <-- BranchB

in all three cases, the resulting code of the merge is the same, just the history is different.