Expenses, yes.

Depreciation, maybe.

In my opinion, if there is a contract of ownership between the taxpayer and the person who holds the title that the taxpayer, then the taxpayer can claim depreciation.

"someone else's name who helped her to acquire the truck"

That makes it sound like her truck.  The title is in someone else's name and that other someone actually paid for the truck with their own dollar bills?

Correct, the truck is not under her name. She is paying back the owner in a monthly basis. 

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@cedurand wrote:

. She is paying back the owner in a monthly basis. 

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That makes it sound like she is purchasing it to me.

Yeah, otherwise with that slant on things nobody would be able to depreciate a vehicle if it was financed by the bank.

This makes me a bit uncomfortable: "She has been paying the truck and all related expenses using her LLC. Can she deduct all the truck expenses under her schedule C?"

in concert with: "She is paying back the owner in a monthly basis."

Because it isn't clear if there is a Lease or Loan agreement between these two parties. At first, it seems like she was making the Payments to the lender, but with both parts, she is paying the other person directly.

Are you trying to write off the Truck Payments?

Yes, and all other expenses related to the truck so it can be in business. My doubt is that the truck is not under the llc neither my client's name. It is under another individual's name that lent the money to my client. 

If it was lent to taxpayer, why is the truck not in the taxpayers name?

Let's review basics: you don't "write off" as expense the Payment amount that is servicing the loan principal balance. Think of this as Expenditure (cash flow) but not Expense. Expense is, for instance, Tires and Fuel = Poof! All used up quickly. Or, your office electricity bill.

Investments in an Asset is not Expensed. The fact that it is paid by getting a loan does not make the Loan Payment principal portion an Expense, even though it is being paid monthly. It is paying down Debt. The Debt was used to acquire an Asset. You treat each of those separately and per the tax regulation that applies.

Let's take just one example. Let's pretend that a small business buys a construction trailer for $2,000 and this qualifies for treatment as expense write off under the de minimis property rule:

"The de minimis safe harbor is simply an administrative convenience that generally allows you to elect to deduct small-dollar expenditures for the acquisition or production of property that otherwise must be capitalized under the general rules."

Let's say they paid $500 down and financed the other $1,500 to be paid monthly over three years.

The Tax write off is $2,000.

The loan interest for business property purchase is Expense.

The remaining amount of the payments (payment minus interest) is not an expense, not a write off, and doesn't even go on the tax return for those three years. It's paying down debt.

The same is true for paying down a credit card balance. A business credit card carrying a balance means you might be able to include the interest in expenses, but fees and the balance payments are paying down debt and not expense. You didn't buy anything for that share of those payments, in other words. It's just debt.

These people with this truck "arrangement" need some legal, insurance and financial guidance. It seems they have some weird handshake arrangement and not a true business agreement. And the person you find to help them should also be able to mentor you.

What about depreciate it in full (45K) by using section 179?

Seems to me there needs to be a truck lease or promissory note between the buyer and seller to clear this up then you know what you can do.

Is the owner of the truck considering it a lease, reporting the payments she makes as rental income and depreciating the truck (probably showing a Schedule C loss)?  This used to be a popular tax shelter, especially in the days of investment credit. 

"What about depreciate it in full (45K) by using section 179?"

You don't even know who Owns this Truck!