Asmerri, because you asked for the specific date-range of your friend's Pettibone-backmark button, I'll pick up from where Creskol left off, quoting from the McGuinn-&-Bazelon book on button backmark dating.
The book says:
"Pettibone Mfg. Co., Cincinatti [Ohio] -- James H. Pettibone was a clerk with John Boner [a dealer of military & fancy goods] from 1864-1871. He took over the business in 1872. [...] It lasted to 1975. The firm did not make buttons."
Therefore, your friend's button can date anywhere from 1872 to 1975. But I believe it is most likely to have been made sometime between 1872 and the first part of the 1900s, when the Texas State Militia became part of the US National Guard and therefore quit using Texas buttons.
Important info for anybody here who doesn't already know:
The name given on the VAST MAJORITY of button backmarks is NOT the name of the button's manufacturer... but instead is the name of a button DEALER or a clothing-maker or a clothing dealer. Actual button-makers (such as Scovill Mfg. Co. and the Waterbury Button Co.) offered their commercial-business customers the option of having the customer's business-name be the backmark instead of the button-maker's name. Such backmarks were known as a "customized" backmark. As the backmark book says, Pettibone never actually MADE any buttons. The backmark saying Pettibone Mfg. Co. is just one example of many hundreds of "customized" backmarks for non-buttonmaking businesses, such as clothing-makers and dealers, tailors, etc. The "customized" backmark was a form of advertising for those business.
Long ago, I was shocked to discover that a civil war era Louisiana State Seal button with a "Hyde & Goodrich - New Orleans" backmark I'd dug was NOT a Confederate-made button. Hyde & Goodrich never manufactured any buttons -- all buttons with that backmark were made by the Scovill Manufacturing Company, located in Connecticut. Similarly, I was surprised to learn that none of the many buttons with a Horstmann backmark were manufactured by that firm. The Horstmann Company was merely a DEALER of buttons -- although it did manufactured military uniforms, hats, etc.
A Modern example of those "customized" backmarks is the canned vegetables you buy at your local grocery store which have the store's name on the can's label. The store is a dealer/seller of them, not a manufacturer.