Is one allowed to inflate a time-sheet for an employer when one failed to bill previously for work and/or reimbursements?
It would be permitted to inflate a time-sheet if the employer certainly owes the relevant amount of money, and there is no other (relatively convenient) way of getting it paid.
We find serveral instances in which it is permitted to lie in order to save oneself from financial harm. This is clear from the Gemara in Yoma (83b), in which stolen goods were recovered by telling a falsehood, and from Bava Metzia 75b, which states that a worker who quits his job in an unlawful manner may be falsely promised extra wage (see Shulchan Aruch, Choshen Mishpat 333:5). despite promising to double their wages, the employer need not pay more than their original salary. Rivash (475) extends this principle to other cases in which someone wishes to unlawfully inflict financial losses on his fellow.
Indeed, the primary source for lying to avoid a loss is the teaching of the Gemara (Nedarim 27b) whereby it is permitted to make a false vow in order to get out of paying unlawful taxes. As Shulchan Aruch (Yoreh De’ah 232:15) rules, if someone is under physical or financial damage threat, he is thus permitted to make a false oath to avert the damage.
We further find that it is permitted for someone to collect ‘difficult’ debts through forms of trickery. One may feign to sell an item to a borrower for the amount owed; after taking the money for the ‘sale’, there is no obligation to hand over the promised product—instead, the money is collected to pay the debt (see Shulchan Aruch 204:11; Rema 190:6).
However, declaring working hours can be distinguished from the cases above, in which somebody else is acting unlawfully, and it is permitted to use falsehood to ‘save oneself’ from harm. In the case of declaring hours, assuming that the employer was not at fault in not paying for the work, one is not really ‘saving oneself’ from unlawful harm.
Yet, if inflating the time sheet is the only (convenient) means of saving from loss, there is room to be lenient. The Torah prohibition of speaking falsehoods applies only in beis din, or possibly in matters of causing others monetary harm, and in this case, where the employer actually owes the money and no harm is being caused, it would be permitted to inflate the hours on the sheet.