Is it true that Umar ibn al-Khattab said: "I do not ask Allah for a light burden, but rather I ask Him for a strong back"?

We have not found a basis for this narration. The fundamental principle is that a Muslim may ask Allah for ease and alleviation, for Allah Almighty has bestowed upon this nation alleviation and removed from it the burdens, as He says: ﴿Allah wishes to lighten your burden; and man was created weak﴾ and His saying: ﴿Now Allah has lightened your burden, for He knows that there is weakness in you﴾. The resolute messengers prayed for alleviation, such as Moses (peace be upon him): ﴿He said, "My Lord, expand for me my breast, And ease for me my task"﴾. And among what Allah Almighty guided the believers to is His saying: ﴿Our Lord, lay not upon us a burden like that which You laid upon those before us. Our Lord, and burden us not with that which we have no ability to bear.﴾