I think in second sentences there must be 'been'...B. we will have been sent it by the first week of May. In second there is assurance underlined by using 'will have been'...
"B" is a future perfect tense which I think the correct one. I'm not sure if native speakers often use this tense. Instead, they just simply say "We will send it sometime in May."
" We will have sent (the package) by the first week of May." Meaning, a completed future action with future barrier.